# Volume of a Cube Cuboid Cylinder

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## Volume of a Cube Cuboid Cylinder

### Cuboid

1) volume of cuboid = l × b × h. Since l × b is the area of its base we can also say that,
Volume of cuboid = area of the base × height.

### Cube

1) The cube is a special case of a cuboid, where l = b = h.
Hence, volume of cube = l × l × l = l3

### Cylinder

1) Volume of cylinder = area of base × height = πr2 × h = πr2h.

### Volume and Capacity

There is not much difference between these two words.
(a) Volume refers to the amount of space occupied by an object.
(b) Capacity refers to the quantity that a container holds.

### Example 1:

Find the height of a cuboid whose volume is 275 cu. cm and base area is 25 sq. cm .

### Solution:

Volume of a cuboid = Base area × Height
Hence height of the cuboid = Volume of cuboid/Base area = 275/25 = 11 cm
Height of the cuboid is 11 cm.

### Example 2:

A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 cu. m ?

### Solution:

Volume of one box = 0.8 cu. m
Volume of godown = 60 × 40 × 30 = 72000 cu. m
Number of boxes that can be stored in the godown = Volume of the godown / Volume of one box
=60 × 40 × 30 / 0.8 = 90,000
Hence the number of cuboidal boxes that can be stored in the godown is 90,000.

### Example 3:

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder.

### Solution:

A cylinder is formed by rolling a rectangle about its width. Hence the width of the paper becomes height and radius of the cylinder is 20 cm.
Height of the cylinder = h = 14 cm
Radius = r = 20 cm
Volume of the cylinder = V = π2h = π × 20 × 20 × 14 = 17600 cu. cm
Hence, the volume of the cylinder is 17600 cu. cm.

### Example 4:

A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.

### Solution:

Length of the paper becomes the perimeter of the base of the cylinder and width becomes height.
Let radius of the cylinder = r and height = h
Perimeter of the base of the cylinder = 2πr = 11 or r = 7/4 cm
Volume of the cylinder = V = πr2h = π × (7/4)×(7/4)× 4 cu. cm = 38.5 cu. cm.
Hence the volume of the cylinder is 38.5 cu. cm.