Question

describe volume of solids in brief


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Answer 1

Volume Of Solids

The total space occupied by a solid is called its volume. Volume is measured in cu.mm (mm³), cu.cm (cm³), cu.m (m³), etc.

The length, breadth and height of the cube given in attachment are of 1 cm each. So, its volume is said to be 1 cm³.

Volume Of Cuboid:

Volume of a cuboid is calculated as product of area of its rectangular base and height.

∴Volume of cuboid = Area of base × height

                             ⇒ l × b × h

Volume Of Cube:

In the case of a cube, its length,breadth and height are equal i.e l = b = h.

∴Volume of cube = l × b × h

                              ⇒ l × l × l

                        ⇒ l³

Answer 2

$\mathbb{\underline{VOLUME\:OF\:SOLIDS}}$

Volume is the space occupied by a solid .

The volume of any body can be found out by knowing the area of cross section and the height of the body .

Given below are the volumes of some special solids .

$\mathcal{\underline{CUBOID}}$

A cuboid is a solid having rectangular cross section .

The volume of the cuboid = area of cross section × height ,

Since area of cross section is length × breadth , the volume will be :

V = length × breadth × height .

$\mathcal{\underline{CUBE}}$

Cube is a solid having equal length , breadth and height .

Volume = area of cross section × height .

Let the side be a .

Volume = a × a × a

⇒ Volume = a³ .

$\mathcal{\underline{CYLINDER}}$

A cylinder is a solid having circular cross section .

Volume = πr² × h

⇒ Volume = πr²h

$\mathcal{\underline{SPHERE}}$

A sphere is a solid having circular cross section .

Volume = 4/3 πr³.

$\mathcal{\underline{CONE}}$

Volume of a cone having same radius and height is one-third of the cylinder .

Volume = 1/3 πr²h