A hemispherical tank full of water is emptied by a pipe at the rate of 3 4 7 litters per second. How much time will it take to empty half the tank, if it is 3 m in diameter.(Take π = 22 7 )

Radius of base of tank = D 2 = 3 2 m Volume of tank = 2 3 πr 3 = 2 3 × 22 7 × 3 2 3 = 99 14 m 3 = 99 14 × 1000 l i t r e s = 99000 14 l i t r e s Volume of water to be emptied = 1 2 × volume of tank = 1 2 × 99000 14 l i t r e s = 99000 28 l i t r e s Time taken to empty 3 4 7 = 25 7 l i t r e s = 1 s e c Time taken to empty 1 l i t r e s = 7 25 s e c Time taken to empty 99000 28 l i t r e s = 99000 28 × 7 25 = 69300 700 = 990 s e c = 990 60 m i n = 16 . 5 m i n Time taken to empty half tank is 16 minute and 5 second.

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.

The height of the cone, h = 24 cm The radius of the base of the cone, r = 6 cm The volume of the cone = 1 3 r 2 h = 1 3 π 6 2 × 24 cm 3 Given that, a child reshapes the cone in the form of a sphere. Let, the radius of the sphere is r ' cm So the volume of the sphere = 4 3 π r ' 3 Since the cone is reshaped into the sphere, So, the volume of the sphere = the volume of the cone ∴ 4 3 π r ' 3 = 1 3 π × 6 × 6 × 24 ⇒ r ' 3 = π × 6 × 6 × 24 × 3 3 × 4 × π ⇒ r ' = 6 × 6 × 6 3 = 6 cm Hence, the radius of the sphere is 6 cm .

A hemispherical tank full of water is emptied by a pipe at the rate of 3 4 7 litters per second. How much time will it take to empty half the tank, if it is 3 m in diameter.(Take π = 22 7 )

Radius of base of tank = D 2 = 3 2 m Volume of tank = 2 3 πr 3 = 2 3 × 22 7 × 3 2 3 = 99 14 m 3 = 99 14 × 1000 l i t r e s = 99000 14 l i t r e s Volume of water to be emptied = 1 2 × volume of tank = 1 2 × 99000 14 l i t r e s = 99000 28 l i t r e s Time taken to empty 3 4 7 = 25 7 l i t r e s = 1 s e c Time taken to empty 1 l i t r e s = 7 25 s e c Time taken to empty 99000 28 l i t r e s = 99000 28 × 7 25 = 69300 700 = 990 s e c = 990 60 m i n = 16 . 5 m i n Time taken to empty half tank is 16 minute and 5 second.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2020>Q 11

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

Earn 100

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $14 mm$ and the diameter of the capsule is $5 mm$ . Find its surface area.

Important Questions on Surface Areas and Volumes

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2018>Q 1

Volume of cuboid $=$ Length $\times$ Breadth $\times$ Height.

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2018>Q 2

The edge of a cube is

5 cm

. What will be its volume?

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2018>Q 3

If

V

is the volume of cuboid whose length is

a

, breadth is

b

and height is

c

and

S

is its total surface area, then prove that

\frac{1}{V} = \frac{2}{S} [\frac{1}{a} + \frac{1}{b} + \frac{1}{c}]

.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2018>Q 4

Two cubes each of

15 cm

sides are joined end to end. Find the total surface area of the resulting cuboid.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2018>Q 5

A iron sphere of radius

8 cm

is melted then recasted into small spheres each of radius

1 cm

. Find the number of small spheres.

HARD

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2019>Q 7

The radii of the ends of a frustum of a cone $45$ cm high are $28$ cm and $7$ cm respectively, find the volume.

HARD

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2019>Q 8

A hemispherical tank full of water is emptied by a pipe at the rate of $3 \frac{4}{7}$ litters per second. How much time will it take to empty half the tank, if it is $3$ m in diameter.(Take $π = \frac{22}{7}$ )

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2020>Q 9

The formula of volume of cylinder is: