**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**

Name | Volume | Nomenclature |

Cube | 1^{3} | 1 = Edge of the cube |

Cuboid | lbh | 1 = Length, b = Breadth, h = Height |

Cylinder | 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 cm^{2}

Volume of cuboid = 1bh

= 9 × 3 × 4

= 108 cm^{3}

**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?

**Solution:**

radius = 3 cm

Height = 7 cm

Lateral surface area of cylinder

= 2 × 3.14 × 3 × 7

= 131.88 cm^{2}

Volume of cylinder

= 3.14 × 3 × 3 × 7

= 197.82 cm^{3}

**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 = s^{3} = 4^{3} = 64 cm^{3}

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