NCERT Solution Class 8th Maths Chapter 9 Mensuration Exercise 9.3

(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: We find an area when a region is covered by a boundary, such as the outer and inner surface area of a cylinder, a cone, a sphere and the surface of a wall or floor.

When the amount of space is occupied by an object such as water, milk, coffee, tea, etc., then we have to find out the volume of the object.

(a) Volume (b) Surface area (c) Volume

Solution:

Yes, we can say that volume of cylinder B is greater, since radius of cylinder B is greater than that of cylinder A.
Find Volume for cylinders A and B
Diameter of cylinder A = 7 cm
Radius of cylinder A = 7/2  cm
And Height of cylinder A = 14 cm
Volume of cylinder A = πr²h
=  (22/7 )×(7/2)×(7/2)×14 = 539
Volume of cylinder A is 539  cm3
Now, Diameter of cylinder B = 14 cm
Radius of cylinder B =  14/2 = 7 cm
And Height of cylinder B = 7 cm
Volume of cylinder B = πr²h
= (22/7)×7×7×7 = 1078
Volume of cylinder B is 1078 cm³

Find surface area for cylinders A and B
Surface area of cylinder A =  2πr(r+h )
= 2 x 22/7 x 7/2 x (7/2 + 14) = 385
Surface area of cylinder A is385 cm³
Surface area of cylinder B =  2πr(r+h)
= 2×(22/7)×7(7+7) = 616
Surface area of cylinder B is 616 cm³
Yes, cylinder with greater volume also has greater surface area.

Solution: Given, Base area of cuboid = 180 cm³ and Volume of cuboid = 900 cm³
We know that, Volume of cuboid = lxbxh
900 = 180×h (substituting the values)
h= 900/180 = 5
Hence the height of cuboid is 5 cm.

Solution:

Given, Length of cuboid, l = 60 cm, Breadth of cuboid, b = 54 cm and
Height of cuboid, h = 30 cm
We know that, Volume of cuboid = lxbxh = 60 ×54×30  = 97200 cm³
And Volume of cube = (Side)³
= 6×6×6 = 216 cm³
Also, Number of small cubes =  volume of cuboid / volume of cube
= 97200/216
= 450
Hence , required cubes are 450.

Solution:

Given: Volume of cylinder = 1.54 m³ and Diameter of cylinder = 140 cm
Radius  ( r )=  d/2 = 140/2  = 70 cm
Volume of cylinder = πr²h
1.54 = (22/7)×0.7×0.7×h
After simplifying, we get the value of h that is
h = (1.54×7)/(22×0.7×0.7)
h = 1
Hence, height of the cylinder is 1 m.

Solution:

Given, Radius of cylindrical tank, r = 1.5 m and Height of cylindrical tank, h  = 7 m
Volume of cylindrical tank, V =  πr²h
= (22/7)×1.5×1.5 ×7
= 49.5  cm³
= 49.5×1000 liters = 49500 liters
[∵ 1 m3= 1000 liters]
Hence, required quantity of milk is 49500 liters.

Solution:

(i) Let the edge of cube be “ l” .

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

(ii) Volume of cube, V = l3

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

Solution:

Given, the volume of the reservoir = 108 m³
Rate of pouring water into cuboidal reservoir = 60 liters/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 the 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
It will take 30 hours to fill the reservoir.