Mensuration - 8th math

Mensuration Class Eighth Math NCERT 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.

Solution

(a) To find how much it can hold.

Volume Answer

Explanation

To find how much it can hold, volume of given tank is required to be calculated.

(b) Number of cement bags required to plaster it.

Total surface area. Answer

Explanation

Since plaster is to be done on its surface, thus total surface area is to be calculated.

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

Volume of smaller tanks and volume of given larger tank. Answer

Explanation

Volume of larger tank divided by the volume of one smaller tank will give the number of tanks that can be filled with water from it.

Mensuration Class Eighth Math NCERT Exercise 11.4 Question (2) Diameter of cylinder A is 7cm, and the height is 14cm. Diameter of cylinder B is 14cm and height is 7cm 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?

Solution

We know that volume of a cylinder is πr²h

This means that cylinder which has greater radius will have greater volume and vice-versa. Thus, cylinder with 14cm i.e. cylinder B will have greater volume than cylinder having 7cm diameter i.e. of cylinder A.

That is cylinder B has greater volume.

Calculation of volume of cylinder A

Given, diameter = 7cm

Thus, radius (r) = 7/2 = 3.5cm

And height (h) = 14cm

Thus, volume = ?

We know that volume of a cylinder is πr²h

Thus, volume of cylinder A

= 22 × 12.25 × 2

= 539 cm³

Thus volume of cylinder A = 539 cm³

Calculation of surface area of cylinder A

We know that, Total surface area of a cylinder = 2πr(r + h)

Thus, total surface area of cylinder A

= 2 × 22 × 0.5 × 17.5

= 22 × 17.5

= 385 cm²

Thus, total surface area of cylinder A = 385cm²

Calculation of Volume of cylinder B

Given, diameter = 14cm

Thus, radius (r) = 14/2 = 7cm

And height (h) = 7cm

Thus, volume = ?

We know that volume of a cylinder is πr²h

Thus, volume of cylinder A

= 22 × 49

= 1078 cm³

Thus volume of cylinder A = 1078 cm³

Calculation of surface area of cylinder B

We know that, Total surface area of a cylinder = 2πr(r + h)

Thus, total surface area of cylinder B

= 2 × 22 × 14

= 616 cm²

Thus, total surface area of cylinder B = 616cm²

Thus, cylinder having greater volume has greater surface area also.

Thus, cylinder B has greater volume and surface area both Answer

Mensuration Class Eighth Math NCERT Exercise 11.4 Question (3) Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?

Solution

Given, area of base of a cuboid = 180 cm²

And volume of the cuboid = 900 cm³

Thus, height (h) = ?

We know that, Volume of a cuboid = length × breadth × height

⇒ Volume of cuboid = Area of cuboid × height

⇒ 900cm³ = 180cm² × height

⇒ height

⇒ height = 5 cm

Thus, height of the given cuboid = 5 cm Answer

Mensuration Class Eighth Math NCERT Exercise 11.4 Question (4) A cuboid is of dimensions 60cm × 54cm × 30cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Solution

Given, dimenstion of a cuboid = 60cm × 54cm × 30cm

And side of a cube = 6cm

Thus, number cube can be placed in the given cuboid = ?

We know that, Volume of the given cuboid = length × breadth × height

Thus, Volume of the given cuboid = 60cm × 54cm × 30cm

= 97200 cm³

And we know that, volume of a cube = side³

Thus, volume of the given cube = (6 cm)³

= 216 cm³

Now, number of cube can be placed in the given cuboid = volume of the cuboid/volume of the cube

= 450

Thus, number of given cube which can be placed in the given cuboid = 450 Answer

Mensuration Class Eighth Math NCERT Exercise 11.4 Question (5) Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?

Solution

Given, volume of a cylinder = 1.54 cm³

And diameter of the base of the cylinder = 140cm

Thus, radius of the base of the cylinder (r) = 140/2 =70cm

= 70/100m = 0.7 m

Thus, height of the cylinder = ?

We know that, Volume of a cylinder = π r² h

⇒ 1.54 = 22 × 0.1 × 0.7 × h

⇒ 1.54 = 1.54 × h

⇒ h = 1 m

Thus, height of the given cylinder = 1m Answer

Mensuration Class Eighth Math NCERT Exercise 11.4 Question (6) A milk tank is in the form of cylinder whose radius is 1.5m and length is 7m. Find the quantity of milk in litres that can be stored in the tank?

Solution

Given, radius of the milk tank = 1.5 m

And length of the milk tank = 7m

Thus, quantity of milk in litres can be stored in the tank = ?

The quantity of milk in litres can be stored in the tank = Volume of the milk tank in cubic meter × 1000

We know that, Volume of a cylinder = π r² h

Thus, volume of the given cylindrical milk tank

= 22 × 2.25 m³

= 49.5 m³

Thus, volume of milk tank = 49.5 m³

Now, we know that, 1 cubic meter = 1000 litre

Thus, 49.5 cubic meter = 49.5 × 1000 litre

= 49500 litres

Thus, quantity of milk in litres can be stored in the tank = 49500 litres Answer

Mensuration Class Eighth Math NCERT Exercise 11.4 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?

Solution

Let the edge of a cube = a

Now, we know that, Surface area of a cube = 6 a²

And when the edge is doubled, i.e. edge = 2a

Increase in surface area of a cube when each side is doubled

Thus, surface area of the cube = 6 (2a)²

= 6 × 4 a²

= 4 × 6a²

Thus, it is clear that if each edge of a cube is doubled, its surface area will increase by 4 times.

Increase in volume of a cube when each side is doubled

We know that, Volume of a cube = a³

Thus, when side a = 2a

Thus, volume of the cube = (2a)³

= 8 a³

Thus, clearly if each edge of a cube is doubled, its volume will increase 8 times.

Thus, when each edge of a cube is doubled its surface area will increase 4 times and volume will increase 8 times. Answer

Mensuration Class Eighth Math NCERT Exercise 11.4 Question (8) Water is pouring into a cuboidal 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.

Solution

Given, volume of the reservoir = 108 m³

= 108 × 1000 litre

= 10800 litre

And given rate of pouring of water into reservoir = 60 litre per minute

Thus, time to fill the reservoir in hours = ?

∵ time takes to fill 60 litre of water = 1 minute

∴ time will take to fill 1 litre of water = 1/60 minute

∴ time will take to fill 108000 litre of water minute

= 1800 minute

= 1800/60 hour = 30 hour

Thus, time to fill the given reservoir = 30 hour Answer