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Capacity

In daily life, we use the terms ‘volume’ and ‘capacity’ interchangeably. However, there is a slight
difference between the two terms.

(a) Volume denotes the amount of space occupied by an object.
(b) Capacity means the quantity that a container holds.
The quantity of anything that a container can hold is called its capacity. When we say that the
capacity of a water tank is 1000 L, we mean that the tank can store 1000 L of water. If the water
tank is completely filled with water, then the volume of water in the tank is 1000 L (= capacity of
water tank). But when the water tank is half-filled with water, the volume of water in the tank is
500 litres, but the capacity of the tank is still 1000 litres.

Relation between litre and m 3
1 mL = 1 cm 3

3
1 m = 1 m × 1 m × 1 m = 100 cm × 100 cm × 100 cm
3
= 1000000 cm = 1000000 mL = 1000 L
Example 32: Find the capacity of a cuboidal water tank, in litres, whose dimensions are 4.2 m,
3 m and 1.8 m.
Solution: As per the given dimensions, the water tank is cuboidal.

\ The capacity of the water tank = Length × breadth × height
= 4.2 m × 3 m × 1.8 m = 22.68 m 3
= 22.68 × 1000 L (Q 1 m = 1000 L)
3
= 22680 L
Thus, the capacity of the water tank is 22680 litres.
Example 33: Find the capacity in litres of a cylindrical vessel whose base radius is 77 cm, and
height is 120 cm. (Round off to whole numbers)

Solution: Base radius of a cylindrical vessel, r = 77 cm, and height of cylindrical vessel, h = 120 cm.
2
\ Volume of the vessel = pr h
22
= × 77 cm × 77 cm × 120 cm = 22 × 11 cm × 77 cm × 120 cm
7
= 2236080 cm 3
3
= 2236080 mL (Q 1 cm = 1 mL)
2236080
.
= L = 2236 08 L (Q 1000 mL = 1 L)
1000
Thus, the capacity of the cylindrical vessel is 2236.08 ≈ 2236 L.

Maths Talk

The diameter and height of cylinder A are 7 cm, and 14 cm respectively. The diameter and height of cylinder
B are 14 cm and 7 cm respectively. Without doing any calculations can you suggest which cylinder’s capacity
is greater? Verify it by finding the volume of both cylinders.
Also, check whether the cylinder with greater volume also has a greater surface area.

253 Mensuration