Page 181 - Maths Skills - 8

Mensuration 179

The following table enlists the interrelations among various other units of volume:

Units of Length Units of Volume

1 cm = 10 mm 1 cm = (10 × 10 × 10) mm 3 = 1000 mm 3
3
1 dm = 10 cm 1 dm = (10 × 10 × 10) cm 3 = 1000 cm = 1 L
3
3
1 m = 10 dm 1 m = (10 × 10 × 10) dm 3 = 1000 dm = 1000 L
3
3
1 m = 100 cm 1 m = (100 × 100 × 100) cm 3 = 1000000 cm 3
3

For measuring the volume of liquids such as water, milk, oil, etc., we normally use the units litres (L) and
millilitres (mL).
1 litre = 1 dm = 1000 cm 3
3
1 1
1 millilitre = litre = × 1000 cm = 1 cm 3
3
1000 1000
Fact-o-meter

� Volume of cuboid = l × b × h cubic unit. � Volume of cube = a cubic unit.
3
� While calculating the volume of a cuboid or a cube, its length, breadth and height must be taken in the
same unit.
� Volume is referred to solid/filled 3-D object.
� Capacity is referred to hollow 3-D object.
� Volume refers to the amount of space occupied by an object. Volume Capacity
� Capacity refers to the quantity that a container holds. (Filled) (Empty)

Let’s Attempt

Example 1: Find the volume of a cuboid whose length, breadth and height are 15 cm, 11 cm and 7 cm
respectively.
Solution: Given, l = 15 cm, b = 11 cm and h = 7 cm.
Volume of a cuboid (V) = l × b × h = 15 cm × 11 cm × 7 cm = 1155 cm .
3
Example 2: A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 l of water, what is
its length?
Solution: Given, b = 90 cm and h = 40 cm. Let the length be l cm.
Volume of water tank (V) = l × b × h = l × 90 × 40 = 3600 l cm .
3
The volume of water contained by the tank = 576 l = 576000 cm 3 [ 1 l = 10 cm ]
3
3
576000
Now, 3600 l = 576000 ⇒ l = = 160 cm
3600
Hence, the length of the water tank is 160 cm.