Page 237 - ICSE Math 8

22 Volume and Surface Area

of Solids

Key Concepts

• Volume of Solids • Cylinder
• Surface Area of Solids • Volume of a Cylinder

Solid figures like cube, cuboid and cylinders have three dimensions, i.e., they are 3D in structure. All such
figures occupy space. In this chapter, we will learn about the measurement of space occupied by some solid
figures. We will also deal with surface area of these figures.

Volume of Solids
1 cm
The measure of the space occupied by a solid body is called its volume. The standard unit
3
of volume is 1 cm , which means volume occupied by a cube of side 1 cm. 1 cm
1 cm

Volume of a cuboid
h
A cuboid is a solid which consists 6 rectangular faces, 12 edges and 8 vertices.
Volume of a cuboid = Length × Breadth × Height b
l
= l × b × h cubic units
With the help of the given formula of volume of Conversion of Units
a cuboid we have, Length units Volume units
3
3
Volume V 1 cm = 10 mm 1 cm = 1,000 mm = 1 mL
Length = ⇒ l =
3
3
Breadth × Height b × h 1 dm = 10 cm 1 dm = 1,000 cm = 1 L
3
3
1 m = 10 dm 1 m = 1,000 dm = 1,000 L
Breadth = Volume ⇒ b = V 1 m = 100 cm 1 m = 10 cm 3
3
6
Length × Height l × h
3
3
1 litre = 1 dm = 1,000 cm = 1,000 mL
Volume V 1 kL = 1,000 L
Height = ⇒ h =
Length × Breadth l × b
Volume of a Cube
A cube is a solid which consists of 6 square faces, 12 edges and 8 vertices.
For a cube, Length = Breadth = Height
3
Volume (V) of a cube = (edge × edge × edge) cm or (l × l × l) cm 3
3
⇒ V = (edge) or V = l 3 l
3
2
Example 1: The volume of a cuboid is 440 cm and the area of the base is 88 cm . Find its height.
3
Solution: Volume of cuboid = 440 cm , Area of base = 88 cm 2
Volume of cuboid 440
Height of cuboid = = = 5 cm
Area of base 88

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