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.

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 1 V = 2 S 1 a + 1 b + 1 c .

Given: ' V ' is the Volume of the cuboid, ' S ' is the Surface area of the cuboid and a × b × c are the dimensions of the cuboid. To prove: 1 V = 2 S 1 a + 1 b + 1 c . We know that, S = 2 a b + b c + c a and V = a b c 1 V = 1 a b c Multiply the numerator and denominator by S . ⇒ 1 V = S S a b c ⇒ 1 V = 2 a b + b c + c a S a b c {Since, S = 2 a b + b c + c a } ⇒ 1 V = 2 S a b a b c + b c a b c + c a a b c ⇒ 1 V = 2 S 1 c + 1 a + 1 b Re-arranging the terms, ⇒ 1 V = 2 S 1 a + 1 b + 1 c . Hence, proved.

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.

Two cubes each of 15 cm sides are joined end to end. Find the total surface area of the resulting cuboid.

When the two cubes each of 15 cm edge are joined end to end, we get a cuboid of dimensions Length l = 15 cm + 15 cm = 30 cm Breadth b = 15 cm Width h = 15 cm Surface area of resulting cuboid is: = 2 ( lb + bh + hl ) = 2 ( 30 × 15 + 15 × 15 + 15 × 30 ) cm 2 = 2 ( 1125 ) cm 2 = 2250 cm 2 Hence the surface area of the resulting cuboid is 2250 cm 2

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2019>Q 6

EASY

10th Madhya Pradesh Board

IMPORTANT

Earn 100

Write the formula of volume of a frustum of a cone.

Important Questions on Surface Areas and Volumes

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:

HARD

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Madhya Pradesh Board-2020>Q 10

A cone of height