Mastering Mensuration: Unlocking Geometric Concepts for All

A Comprehensive Guide for Grade 10 and Beyond, Including Beginners, Middle School, and High School Students.

Created byLakshmi Narayana

Last updated 6/2023

English

What you'll learn

Areas related to Circles - Review of Concepts of Area and Perimeter of a Circle, Areas of Sector and Segment of a Circle.
Length of an Arc of a Sector and Areas of Combination of Plane Figures.
Surface Areas and Volumes - Surface Area of Solid Figures, Volume of Solid Figures, Surface Area and Volume of Combination of Solids.
Conversation of Solid from One Shape to Another and Surface Area and Volume of Frustum of a Cone.
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

2 sections • 135 lectures • 15h 24m total length

Session 1 - Introduction10:22
Introduction
Session 1 - Q 15:03
An athlete runs on a circular track of radius 49 m and covers a distance of 3080 m along its boundary. How many rounds has he taken to cover this distance? [Take π=22/7].
Session 1 - Q 27:41
The cost of fencing a circular field at the rate of ₹24 per metre is ₹5280. The field is to be ploughed at the rate of ₹0.50 per m2. Find the cost of ploughing the field[Take π =22/7].
Session 1 - Q 33:25
If the ratio of the circumferences of two circles is 3 : 1, then find the ratio of their areas.
Session 1 - Q 44:24
If the perimeter of a protractor is 72 cm, then calculate its area.
Test your understanding
Home Assignment
Session 2 - Introduction5:53
Sector and Areas of Sector
Session 2 - Q 12:29
In a circle of radius 21 cm, an arc subtends an angle of 600 at the centre.
Find the area of sector formed by the arc. (Use π = (22 )/7)
Session 2 - Q 25:20
Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π = 3.14).
Session 2 - Q 33:21
What is the perimeter of a sector of a circle whose central angle is 900 and radius is 7 cm?
Session 2 - Q 44:40
Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.
Test your understanding
Home Assignment
Session 3 - Introduction4:23
Area of Segment of a Circle
Session 3 - Q 19:25
Find the area of the segment AYB shown in Fig., if radiusof the circle is 21 cm and ∠AOB = 120°. (Use π = 22/7)
Session 3 - Q 25:50
In a circle with centre O and radius 5 cm, AB is a chord of length 5√3 cm. Find the area of sector AOB.
Session 3 - Q 35:52
A round table cover has six equal designs as shown in the given figure.
If the radius of the cover is 35 cm then find the total area of the design. [Use √3 =1.732 and π= 3.14.]
Test your understanding
Home Assignment
Session 4 - Introduction2:21
Areas of Combinations of Plane Figures:
When combination of circle(or)semi-circle and square (or) rectangle are given
Session 4 - Q 18:18
In figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.
Session 4 - Q 24:22
Find the area of the shaded region in figure, where ABCD is a square of side 14 cm.
Session 4 - Q 37:00
Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π = 3.14)
Session 4 - Q 46:55
In the given figure, ABCD is a trapezium with AB‖DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then, find the area of the shaded region of the figure.
(Use π = 22/7).
Test your understanding
Home Assignment
Session 5 - Introduction1:31
Areas of Combinations of Plane Figures:
When combination of two concentric circles are given
Session 5 - Q 13:44
In the given figure, the area of the shaded region between two concentric circles is 286 cm2. If the difference of the radii of the two circles is 7 cm, find the sum of their radii.
Session 5 - Q 24:35
In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.
Session 5 - Q 38:26
In the given figure, two concentric circles with centre O have radii 21 cm
and 42 cm. If ∠AOB = 600, find the area of the shaded region. (Use π = 22/7)
Session 5 - Q 43:35
Nitika has a circular plot of radius 105 m. he donates a 7 m wide track along its boundary for community track.Find the area of the track. [Take,π=22/7]
Test your understanding
Home Assignment
Session 6 - Introduction1:16
Areas of Combinations of Plane Figures:
When combination of circle and triangle are given
Session 6 - Q 16:50
Find the area of the shaded region in figure, if AC = 20 cm, AB = 15 cm and O is the centre of the circle.
Session 6 - Q 27:32
In the given figure, AOB is a sector of angle 600 of a circle with centre O and radius 17 cm. If AP ⊥ OB and AP = 15 cm, find the area of the shaded region.
Session 6 - Q 36:43
Find the area of the shaded region in figure, if BC = BD = 8 cm, AC = AD = 15 cm and O is the centre of the circle. (Take π = 3.14)
Session 6 - Q 43:51
A memento is made as shown in the figure. Its base PBCR is silver plated from the front side. Find the area which is silver plated. (π =(22 )/7)
Test your understanding
Home Assignment
Session 7 - Introduction1:21
Areas of Combinations of Plane Figures :
When combination of quadrant of circle and triangle (or) square is given
Session 7 - Q 14:47
A square OABC is inscribed in a quadrant OPBQ of a circle as shown in the adjoining figure. If OA = 14 cm, find the area of the shaded region.
Session 7 - Q 28:35
In figure, ABC is a right-angled triangle at A. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
Session 7 - Q 34:04
In figure, APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter of the shaded region.
Session 7 - Q 48:39
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in a given figure. Find the area of the shaded region.
Test your understanding
Home Assignment
Exercise 1 - Q 15:12
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Exercise 1 - Q 26:46
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Exercise 1 - Q 319:46
Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
Exercise 1 - Q 410:30
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Exercise 1 - Q 51:49
Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units (B) p units (C) 4 units (D) 7 units
Exercise 2 - Q 12:42
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Exercise 2 - Q 23:47
Find the area of a quadrant of a circle whose circumference is 22 cm.
Exercise 2 - Q 34:44
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Exercise 2 - Q 412:41
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use π = 3.14)
Exercise 2 - Q 512:22
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(i) the length of the arc (ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Exercise 2 - Q 611:12
A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use π = 3.14 and √3 = 1.73)
Exercise 2 - Q 78:40
A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.
(Use π = 3.14 and √3 = 1.73)
Exercise 2 - Q 89:47
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
Exercise 2 - Q 98:53
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 12.12. Find :
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Exercise 2 - Q 106:19
An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Exercise 2 - Q 116:58
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Exercise 2 - Q 124:47
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)
Exercise 2 - Q 1311:14
A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm2. (Use √3 = 1.7)
Exercise 2 - Q 142:12
Tick the correct answer in the following :
Area of a sector of angle p (in degrees) of a circle with radius R is
(A) p/180 × 2πR (B) p/180 × πR2 (C) p/360 × 2πR (D) p/720 × 2πR2
Exercise 3 - Q 19:56
Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.
Exercise 3 - Q 27:15
Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and AOC = 40°.
Exercise 3 - Q 35:59
Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Exercise 3 - Q 48:32
Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
Exercise 3 - Q 57:27
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.
Exercise 3 - Q 611:45
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral
triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.
Exercise 3 - Q 76:47
In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining
three circles. Find the area of the shaded region.
Exercise 3 - Q 810:51
Fig. 12.26 depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find :
(i) the distance around the track along its inner edge
(ii) the area of the track.
Exercise 3 - Q 98:37
In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Exercise 3 - Q 1014:39
The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region.
(Use π = 3.14 and √3 = 1.73205)
Exercise 3 - Q 117:04
On a square handkerchief, nine circular designs each of radius 7 cm are made
(see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
Exercise 3 - Q 127:53
In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If
OD = 2 cm, find the area of the
(i) quadrant OACB, (ii) shaded region.
Exercise 3 - Q 139:21
In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use = 3.14)
Exercise 3 - Q 146:36
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.
Exercise 3 - Q 1512:29
In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
Exercise 3 - Q 168:20
Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each.

Session 1 - Introduction15:31
Introduction
Session 1 - Q 12:40
Find the number of cubes of side 2 cm which can be cut from a cube of side 4 cm.
Session 1 - Q 23:49
The surface areas of two spheres are in the ratio 16 : 9. Find the ratio of their volumes?
Session 1 - Q 33:06
A rectangular sheet of paper 40 cm × 22 cm is rolled to form a hollow cylinder of height 40 cm. Find the radius of the cylinder.
Test your understanding
Home Assignment
Session 2 - Introduction1:55
Surface Area of a Combination of Solids: When combination of any two figures like - cone (or) sphere (or) hemisphere (or) cylinder (or) cube (or) cuboid is given:
Session 2 - Q 15:53
Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take π = 22/7)
Session 2 - Q 29:03
A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take π = 3.14)
Session 2 - Q 34:39
The decorative block shown in Fig. is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π = 22/7)
Session 2 - Q 44:55
In given fig., from a cuboidal solid metallic block of dimensions 15 cm × 10 cm × 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block. [ Use π = 22/7]
Test your understanding
Home Assignment
Session 3 - Introduction2:18
Surface Area of a Combination of Solids:
When combination of cylinder or half cylinder and sphere (or) hemisphere (or) cube (or) cuboid is given.
When combination of two or more than two figures of same type is given
Session 3 - Q 14:30
Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end (see Fig.). The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.
(Take π = 22/7)
Session 3 - Q 22:57
Two cubes of 5 cm each are kept together joining edge to edge to form a cuboid. Find the surface area of the cuboid so formed.
Session 3 - Q 32:22
The radius of sphere is r cm. It is divided into two equal parts. Find the whole surface of two parts.
Session 3 - Q 43:40
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Test your understanding
Home Assignment
Session 4 - Introduction0:50
ü Volume of a Combination of Solids :
§ When combination of cone and sphere (or) hemisphere (or) cylinder is given.
When combination of sphere (or)hemisphere and cube (or) cuboid is given.
Session 4 - Q 17:30
A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take π = 3.14)
Session 4 - Q 24:09
50 circular plates, each of radius 7 cm and thickness 1/2 cm, are placed one above another to form a solid right circular cylinder. Find the total surface area and the volume of the cylinder so formed.
Session 4 - Q 37:15
A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.
Test your understanding
Home Assignment
Session 5 - Introduction0:46
Volume of a Combination of Solids :
1. When combination of cylinder (or) half cylinder and sphere (or) hemisphere (or) cube (or) cuboid is given.
2. When combination of two or more than two figures of same type is given.
Session 5 - Q 15:50
Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see figure). If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of 300 m3, and there are 20 workers, each of whom occupy about 0.08 m3 space on an average. Then, how much air is in the shed? (Take π = 22/7)
Session 5 - Q 23:29
A juice seller was serving his customers using glasses as shown in figure. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π = 3.14.)
Session 5 - Q 33:13
A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. [Use π = 22/7]
Test your understanding
Home Assignment
Session 6 - Introduction3:45
Conversion of Solid from One Shape to Another.
Session 6 - Q 13:09
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
Session 6 - Q 25:17
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
Session 6 - Q 36:30
A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
Test your understanding
Home Assignment
Session 7 - Introduction1:27
Conversion of Solid from One Shape to Another :
water and canal related problems
Session 7 - Q 16:14
Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use π = 3.14)
Session 7 - Q 24:03
A hemispherical tank full of water is emptied by a pipe at the rate of 3 4/7 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take π = 22/7)
Session 7 - Q 34:31
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
Test your understanding
Home Assignment
Session 8 - Introduction3:44
Frustum of a Cone.
Session 8 - Q 18:11
The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm (see figure). Find its volume, the curved surface area and the total surface area(Take π = 22/7)
Session 8 - Q 23:17
Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see figure). If each cm3 of molasses has mass about 1.2 g, find the mass of the molasses that can be poured into each mould. [Take π = 22/7]
Session 8 - Q 34:45
An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see figure). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. [Take π = 22/7 ]
Session 8 - Q 44:54
A cone is cut by a plane parallel to the base and upper part is removed. If the curved surface area of upper cone is 1/9 times the curved surface of original cone. Find the ratio of line segment to which the cone's height is divided by the plane.
Test your understanding
Home Assignment
Exercise 1 - Q 15:46
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Exercise 1 - Q 27:04
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Exercise 1 - Q 312:00
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Exercise 1 - Q 49:23
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Exercise 1 - Q 58:55
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Exercise 1 - Q 68:50
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Exercise 1 - Q 79:31
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹ 500 per m2. (Note that the base of the tent will not be covered with canvas.)
Exercise 1 - Q 811:02
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
Exercise 1 - Q 96:05
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Exercise 2 - Q 15:20
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
Exercise 2 - Q 29:41
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
Exercise 2 - Q 312:58
A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see Fig. 13.15).
Exercise 2 - Q 411:43
A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by
3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 13.16).
Exercise 2 - Q 58:06
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
Exercise 2 - Q 611:13
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8g mass. (Use = 3.14)
Exercise 2 - Q 710:46
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Exercise 2 - Q 89:20
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and = 3.14.
Exercise 3 - Q 15:56
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Exercise 3 - Q 27:38
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Exercise 3 - Q 38:22
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
Exercise 3 - Q 412:14
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Exercise 3 - Q 512:04
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Exercise 3 - Q 68:27
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?
Exercise 3 - Q 711:26
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
Exercise 3 - Q 811:56
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
Exercise 3 - Q 99:49
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Exercise 4 - Q 15:13
A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
Exercise 4 - Q 25:59
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
Exercise 4 - Q 36:10
A fez, the cap used by the Turks, is shaped like the frustum of a cone (see Fig. 13.24). If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.
Exercise 4 - Q 411:48
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of ₹ 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 8 per 100 cm2. (Take π = 3.14)
Exercise 4 - Q 513:10
A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16 cm, find the length of the wire.

Requirements

Basic elementary math knowledge.
Each chapter includes prerequisite knowledge classes in which the child gains extensive knowledge and a thorough understanding of the chapters.

Description

This course is designed for all middle school and high school students. This course is intended for students under 18 may use the services only if a parent or guardian opens their account, handles any enrolments, and manages their account usage.
It has 135 lectures spanning more than 15 hours of on-demand videos that are divided into 2 sections, and each chapter is a section and further divided into simple sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key. The students are encouraged to solve practise questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand it very well.
It covers 100% video solutions of various problems and situations.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in Mensuration. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning math and never feel that math is troublesome.

Topics covered in the course:

Areas Related to Circles
Surface Areas and Volumes

With this course you'll also get:

Perfect your mathematical skills on Mensuration for better scores.

A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the Mensuration.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of Mensuration and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations as well as job aspirants.
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the solving different real life situations as well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.
These are the people whose jobs require them to solve basic daily math-related problems.

Mastering Mensuration: Unlocking Geometric Concepts for All

What you'll learn

Explore related topics

Course content

Areas Related to Circles69 lectures • 7hr 56min

Surface Areas and Volumes66 lectures • 7hr 28min

Requirements

Description

Who this course is for: