Page 283 - Start Up Mathematics_8 (Non CCE)

18 Mensuration-II (Solid Figures)

Solid figures like cube, cuboid and cylinders have three dimensions, i.e., they H G
are 3-D in structure (Fig. 18.1). All such figures occupy space. In this chapter, A
we will learn about the measurement of space occupied by some solid B
figures. We will also deal with surface area of these figures. E F

Space Region and Volume of the Space Region Formed by a Body D Fig. 18.1 C
The space occupied by a solid is called its space region. If we consider an example of a cistern or water tank,
the part of space enclosed by it is its space region. If the cistern is cuboidal in shape, the space enclosed is the
cuboidal region. If however, the cistern is cylindrical in shape, the space enclosed is the cylindrical region.
The size of the space region of the body is called its volume, or, in other words, the measure of the space
occupied by a solid body is called its volume.

Volume of a cuboid refers to the volume of cuboidal region.

Standard Unit of Volume
3
The standard unit of volume of the space region is 1 cm , which means volume occupied by a cube of
side 1 cm.
Conversion of Units

Formulae Length units 3 Volume units
3
Volume of a cuboid = Length × Breadth × Height 1 cm = 10 mm 1 cm = 1,000 mm = 1 mL
3
3
1 dm = 10 cm 1 dm = 1,000 cm = 1 L
= l × b × h cubic units 1 m = 10 dm 1 m = 1,000 dm = 1,000 L
3
3
6
3
3
3
Volume of a cube = (Edge) or (Side) cubic units 1 m = 100 cm 1 m = 10 cm 3
3
3
1 litre = 1 dm = 1,000 cm = 1,000 mL
1 kL = 1,000 L
Example 1: Find the volume of a cuboid whose length = 12.5 cm, breadth = 9 cm and height = 5.5 cm.
Solution: length (l) = 12.5 cm, breadth (b) = 9 cm and height (h) = 5.5 cm
Volume = l × b × h = 12.5 cm × 9 cm × 5.5 cm = 618.75 cm 3 Remember
Example 2: Find the volume of a cube whose side is 4 cm. Sometimes the term
Solution: Side of cube = 4 cm capacity is used
3
3
Volume of cube = (Side) = (4) = 64 cm 3 instead of volume.
2
3
Example 3: 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
Example 4: Two cubes each of 10 cm edge are joined end to end. Find the
volume of the resulting cuboid.