Volume of Cube, Cuboid and Cylinder

Volume

Volume is the space occupied by any solid figure i.e. the amount of capacity to carry something is the volume of that solid shape. The unit of volume is a cubic unit.

Volume of Cube, Cuboid and Cylinder

NameVolumeNomenclature
Cube131 = Edge of the cube
Cuboidlbh1 = Length, b = Breadth, h = Height
Cylinder \mathrm{\pi r^2h}r = Radius, h = Height

Example 1

There is a shoe box whose length, breadth and height is 9 cm, 3 cm and 4 cm respectively. Find the surface area and volume of the shoe box.

Solution:

Given,

length = 9 cm

Breadth = 3 cm

Height = 4 cm

Area of cuboid = 2(1b + bh + 1h)

= 2(9 × 3 + 3 × 4 + 9 × 4)

= 2(27 + 12 + 36)

= 2(75)

= 150 cm2

Volume of cuboid = 1bh

= 9 × 3 × 4

= 108 cm3

Example 2

If there is a cold drink can whose height is 7 cm and the radius of its round top is 3 cm then what will be the lateral surface area and volume of that cylinder? (\pi=3.14)

Solution:

radius = 3 cm

Height = 7 cm

Lateral surface area of cylinder \mathrm{2\pi rh}

= 2 × 3.14 × 3 × 7

= 131.88 cm2

Volume of cylinder \mathrm{\pi r^2h}

= 3.14 × 3 × 3 × 7

= 197.82 cm3

Example 3

If there is a box of cube shape with the length of 4 cm then what will be the capacity of this box.

Solution:

Given, side = 4 cm

Capacity or volume of the box = s3 = 43 = 64 cm3

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