## Chapter 11 Mensuration Exercise 11.4

Question 1: Given a cylindrical tank, in which situation will you find surface area and in which situation volume.

a) To find how much it can hold.

b) Number of cement bags required to plaster it.

c) To find the number of smaller tanks that can be filled with water from it.

Answer:

a) Volume

b) Surface area

c) Volume

Question 2: Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Answer: The volume of Cylinder B is greater than cylinder A because Cylinder B has a bigger diameter.

Given

Cylinder A

diameter = 7 cm

height = 14 cm

Cylinder B

diameter = 14 cm

height = 7 cm

To find

Volume and surface area of both cylinders

Formula

Volume of cylinder = πr²h

TSA of cylinder = 2πr(h + r)

Working

• Cylinder A

→ Volume

= 22/7 × 3.5 × 3.5 × 14

= 22 × 3.5 × 3.5 × 2

= 22 × 35/10 × 35/10 × 2

= 11 × 7 × 7

= 539 cm³

→ TSA

= 2 × 22/7 × 3.5(14 + 3.5)

= 2 × 22/7 × 3.5 × 17.5

= 2 × 22/7 × 35/10 × 175/10

= 11 × 35

= 385 cm²

• Cylinder B

→ Volume

= 22/7 × 7 × 7 × 7

= 22 × 7 × 7

= 1078 cm³

→ TSA

= 2 × 22/7 × 7(7 + 7)

= 2 × 22 × 14

= 616 cm²

Question 3: Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?

Answer:

Given

Cuboid

base area = 180 cm²

volume = 900 cm³

To find

Height of a cuboid

Formula

General formula of volume = base area × height

Working

= a × 180 = 900

= a = 900/180

= a = 5 cm

Therefore, the height of cuboid is 5 cm.

Question 4: A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Answer:

Given

Cuboid

length = 60 cm

breadth = 54 cm

height = 30 cm

Small cube side length = 6 cm

To find

Number of small cubes that can be placed into cuboid

Formula

Volume of cuboid = lbh

Volume of cube = s³

Working

Volume of cuboid = ?

= 60 × 54 × 30

= 97200 cm³

Volume of small cube = ?

= 6³

= 216 cm³

Number of small cubes that can be fit in cuboid = ?

= 97200/216

= 450 small cubes

Therefore, 450 small cubes can be placed into the cuboid.

Question 5: Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?

Answer:

Given

Cylinder

diameter = 140 cm

volume = 1.54 m³

To find

Height of cylinder

Formula

General formula of volume = base area × height

Area of circle = πr²

Working

Area of base of cylinder = ?

= 22/7 × 70 × 70

= 22 × 10 × 70

= 15400 cm²

Height of cylinder = ?

(1 m³ = 1000000 cm³)

= 15400 × h = 1540000

= h = 1540000/15400

= h = 100 cm

Therefore, the height of cylinder is 100 cm.

Question 6: A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

Answer:

Given

Milk tank in form cylinder

radius = 1.5 m

height = 7 m

To find

The quantity of milk that can be stored in tank

Formula

Volume of cylinder = πr²h

1 m³ = 1000 litres

Working

= 22/7 × 1.5 × 1.5 × 7

= 22 × 1.5 × 1.5

= 22 × 15/10 × 15/10

= 49.5 m³

1 m³ = 1000 litre

= 49.5 × 1000

= 49500 litres

Therefore, the quantity of milk in litres that can be stored in the tank is 49500 litres.

Question 7: If each edge of a cube is doubled,

i) how many times will its surface area increase?

ii) how many times will its volume increase?

Answer:

i)

Let the edge of cube be x cm.

If the edge is doubled = x + x = 2x cm

Original surface area = 6 × (x)²

= 6x² cm²

If the edge is doubled, surface area = 6 × (2x)²

= 24x² cm²

Ratio = If edge is doubled surface area:original surface area

= 24x²:6x²

= 24x²/6x²

= 4 times

Therefore, the new surface area of cube will be 4 times more if the edge is doubled.

ii)

Let the edge of cube be x cm.

If the edge is doubled = x + x = 2x cm

Original volume = (x)³

= x³ cm³

If the edge is doubled, surface area = (2x)³

= 8x³ cm³

Ratio = If edge is doubled volume:original volume

= 8x³:x³

= 8x³/x³

= 8 times

Therefore, the new volume of cube will be 8 times more if the edge is doubled.

Question 8: Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

Answer:

Given

Volume of reservoir = 108 m³

Speed of water flowing = 60 litres per minute

To find

The number of hours it will take to fill reservoir

Formula

1 m³ = 1000 litres

Working

= 108 × 1000

= 108000 litres

Time taken to fill the reservoir = ?

= 108000/60

= 1800 minutes required

1 hour = 60 minutes

= 1800/60

= 30 hours

Therefore, it will take 30 hours to fill the reservoir.

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