# Volume and Capacity

Amount of space occupied by a three dimensional object is called its volume.

Let us try to compare the volume of objects sorrounding us. For example volume of a room is greater than the volume of a chair kept inside it. We use square units to find the area of a region while we use cubic units to find the volume of a solid. Volume of a solid is measured by counting the number of unit cubes it contains.

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Consider 24 unit cubes. These cubes can be arranged in many ways to form a cuboid. Look at the cuboids given below.

Each of these cubes are made of 24 unit cubes. Hence the volume of each is 24 cubic units.

The volume of the first cube is 4 Â´ 3 Â´ 2 cubic units.

The volume of the second cube is 4 Â´ 2 Â´ 3 cubic units.

The volume of the third cube is 3 Â´ 2 Â´ 4 cubic units.

Hence in general we can say that the volume of a cuboid is *l* Â´ * b* Â´ * h* cubic units.

Volume of each cuboid is equal to the product of length, breadth and height of the cuboid.

Volume of cuboid = Area of the base Ã— height

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Consider a cuboid whose measures are :

*l*= 8,

*b*= 3 ,

*h*= 2.

Volume = *l Ã— b Ã— h* = 8 Ã— 3 Ã— 2 = 48 cubic units

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**Cube:**

The cube is a special case of a cuboid, where

*l = b = h*

Volume of cube = *l* Ã— *l* Ã— *l* = *l*3

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Find the volume of the cube whose side is 12 *cm*.

Volume of cube =

== 1728 *cm*^{3}.

**Cylinder:**

Volume of the cylinder can be found out in the same way as that of cuboid. Consider a cylinder of height

*h*units and radius

*r*units. Base of the cylinder is circle in shape.

Therefore, area of the base =

Volume of cylinder = area of base Ã— height

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**Capacity:**

Capacity : The quantity that a container holds.

Capacity is measured in terms of litres

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Find the height of a cuboid whole volume is 375 *cm*^{3} and base area is 5 *cm*^{2}.

Volume of a cuboid = Base area Ã— Height.

Height of the cuboid is 10.71 *cm*.

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A room is in the form of a cuboid has measures 65

*m* Ã— 45 *m* Ã— 35 *m*. How many cuboidal boxes can be stored in it if the volume of one box is 0.5 *m*^{3}?

Volume of box = 0.5 *m*^{3}.

Volume of room = 65 Ã— 45 Ã— 35 = 102375

The number of cuboidal boxes that can be stored in the room is 204750.

a rectangular paper of width 10 *cm *is rolled along its width and a cylinder of radius 15 *cm* is formed. Find the volume of the cylinder.

Width of the paper = height of the cylinder = 10 cm

Radius = 15 cm

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A rectangular piece of paper 15

*cm *Ã— 5 *cm* is folded without overlapping to make a cylinder of height 5 *cm*. Find the volume of the cylinder.

Perimeter of the base of the cylinder

Volume of cylinder

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