NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4 are the part of NCERT Solutions for Class 8 Maths. Here you can find the NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.4.

Ex 11.4 Class 8 Maths Question 1.

Given a cylindrical tank, in which situation will you find the 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) In this situation, we can find the volume.
(b) In this situation, we can find the surface area.
(c) In this situation, we can find the volume.

Ex 11.4 Class 8 Maths 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?

Solution:
Cylinder B has a greater volume.
Verification:
Volume of cylinder A = πr²h

Ex 11.4 Class 8 Maths Question 3.

Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³.

Solution:
Given: Base area of the cuboid = lb = 180 cm²
Volume of the cuboid = 900 cm³
Volume of a cuboid = l × b × h
900 = 180 × h
h = 5 cm
Hence, the height of the cuboid is 5 cm.

Ex 11.4 Class 8 Maths 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?

Solution:
Volume of a cuboid = l × b × h = 60 cm × 54 cm × 30 cm = 97200 cm³
Volume of a cube = (Side)³ = (6)³ = 216 cm³
Number of the cubes placed in the cuboid

Hence, the required number of cubes is 450.

Ex 11.4 Class 8 Maths Question 5.

Find the height of the cylinder whose volume is 1.54 m³ and the diameter of the base is 140 cm.

Solution:
Volume of the cylinder = 1.54 m³

Diameter of the base = 140 cm = 1.4 m

Volume of a cylinder = πr²h

Hence, the height of the cylinder is 1 m.

Ex 11.4 Class 8 Maths Question 6.

A milk tank is in the form of a 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.

Solution:
Here, radius of the tank = 1.5 m
Height of the tank = 7 m
Volume of the milk tank = πr²h
= 22/7 × 1.5 × 1.5 × 7
= 22 × 2.25
= 49.50 m³
Quantity of milk in litres = 49.50 × 1000 L (∵ 1 m³ = 1000 litres)
= 49500 L
Hence, the required quantity of milk is 49500 L.

Ex 11.4 Class 8 Maths 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 each edge of the cube be x cm.
If the edge is doubled, then the new edge = 2x cm
(i) Original surface area of the cube = 6x² cm²
New surface area of the cube = 6(2x)² = 6 × 4x² = 24x²
Ratio = 6x² : 24x² = 1 : 4
Hence, the new surface area will be four times the original surface area.

(ii) Original volume of the cube = x³ cm³
New volume of the cube = (2x)³ = 8x³ cm³
Ratio = x³ : 8x³ = 1 : 8
Hence, the new volume will be eight times the original volume.

Ex 11.4 Class 8 Maths Question 8.

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

Solution:
Volume of the reservoir = 108 m³ = 108000 L [∵ 1 m³ = 1000 L]
Volume of water flowing into the reservoir in 1 minute = 60 L
Time taken to fill the reservoir