NCERT Solutions Class 8 Maths Chapter 11 Mensuration Ex 11.4

NCERT Solutions Class 8 Mathematics 
Chapter – 11 (Mensuration) 

The NCERT Solutions in English Language for Class 8 Mathematics Chapter – 11 Mensuration Exercise 11.4 has been provided here to help the students in solving the questions from this exercise. 

Chapter 11: Mensuration

• NCERT Solution Class 8 Maths Ex – 11.1
• NCERT Solution Class 8 Maths Ex – 11.2
• NCERT Solution Class 8 Maths Ex – 11.3

Exercise – 11.4 

1.Given a cylindrical tank, in which situation will you find surface are 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)
(b) Number of cement bags required to plaster it. (Surface area)
(c) To find the number of smaller tanks that can be filled with water from it. (Volume)

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 – Yes, we can say that volume of cylinder B is greater, since radius of cylinder B is greater than that of cylinder A.
Radius of cylinder A(r) = 7/2 cm = 3.5 cm
Height of cylinder A(h) = 14 cm

Volume of cylinder A = πr²h
= × 3.5 × 3.5 × 7
= 269.5 cm³

Radius of cylinder B (r₁) = 14/2 cm = 7 cm
Height of cylinder B (h₁) = 7 cm
Volume of cylinder B = πr₁²h₁
=   × 7 × 7 × 7 = 1078 cm³

CSA of cylinder A = 2πrh
= 2 × × 3.5 × 14
= 308 cm²

Total surface area (TSA) of cylinder A = 2πr (r + h)
= 2πr² + 2πrh
= (2 × × 3.5 × 3.5) cm² + 308 cm²
= 385 cm²

CSA of cylinder B = 2πr_₁h_₁
= 2 × × 7 × 7
= 308 cm²

Total surface area (TSA) of cylinder B = 2πr₁ (r_₁ + h_₁)
= 2πr_₁²h_₁ + 2πr_₁h_₁
= (2 × × 7 × 7) cm² + 308 cm
= 308 cm² + 308 cm²
= 616 cm²
Yes, the cylinder with greater volume also has a greater surface area.

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

Solution – Base area of cuboid = 180 cm²
Volume of cuboid = 900 cm³
Volume of cuboid = lbh
900 = 180×h (substituting the values)
h= 900/180 = 5
Hence the height of the cuboid is 5 cm.

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 – Length of cuboid, l = 60 cm,
Breadth of cuboid, b = 54 cm and
Height of cuboid, h = 30 cm
Volume of cuboid = lbh
= 60 × 54 × 30
= 97200 cm³
Volume of cube = (Side)³
= 6×6×6 = 216 cm³
Also, the Number of small cubes =  volume of cuboid / volume of cube
= 97200/216
= 450
Hence , the required number of cubes is 450.

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

Solution – Volume of cylinder = 1.54 m³
Diameter of cylinder = 140 cm
Radius  (r)=  d/2 = 140/2  = 70 cm
Volume of cylinder = πr²h
1.54 =   × 0.7 × 0.7 × h
After simplifying, we get the value of h, which is,
h =

h = 1
Hence, the height of the cylinder is 1 m.

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 liters that can be stored in the tank.

Solution – Radius of cylindrical tank, r = 1.5 m
Height of cylindrical tank, h  = 7 m
Volume of cylindrical tank, V =  πr²h
= × 1.5 × 1.5 × 7
= 49.5  cm³
= 49.5×1000 liters = 49500 liters [∵ 1 m³= 1000 litres]
Hence, the required quantity of milk is 49500 litres.

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 –

(i) Let the edge of the cube be “l” .
Formula for Surface area of the cube, A =  6l²
When the edge of the cube is doubled, then
Surface area of the cube, say A’ = 6(2l)²
= 6×4l²
= 4(6l²)
A’ = 4A
Hence, the surface area will increase by four times.

(ii) Volume of a cube, V = l³
When the edge of the cube is doubled, then
Volume of the cube, say V’ = (2l)³ = 8( l³)
V’ = 8×V
Hence, the volume will increase 8 times.

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

Solution – the volume of the reservoir = 108 m³
Rate of pouring water into cuboidal reservoir = 60 litres/minute
=  60/1000  m³ per minute
Since 1 liter = (1/1000 )m³
=  (60×60)/1000 m³ per hour
Therefore, (60×60)/1000 m³ water filled in reservoir will take = 1 hour
Therefore 1 m³ water filled in reservoir will take =  1000/(60×60)  hours
Therefore, 108 m³ water filled in reservoir will take = (108×1000)/(60×60)  hours
= 30 hours
Thus, the number of hours it will take to fill the reservoir is 30 hours.