Question

The capacity of a measuring flask is 1 litre. What will it be in cubic centimeters?
(a) 1 Cubic centimeter
(b) 10 Cubic centimeter
(c) 100 Cubic centimeter
(d) 1000 Cubic centimeter

Answer 1

Hint: Use the relation between the two units of volume Cubic meter and litre given as 1 Cubic meter = 1000 litres as the basic relation. Now, use the unitary method to find the value of 1 litre by dividing both the sides with 1000. Convert meter into centimeter using the relation 1 m = 100 cm and derive the relationship between litre and cubic centimeter to get the answer.

Complete step-by-step solution:
Here we have been provided with the capacity (volume) of a measuring flask equal to 1 litre. We are asked to find the volume in cubic centimeters. Let us see the required relationship.
Now, we know that the S.I unit of volume is cubic meter and 1 Cubic meter is equal to 1000 litres. We can write it mathematically as: -
$\Rightarrow $ 1000 litres = 1 ${{m}^{3}}$
Dividing both the sides with 1000 we get,
$\Rightarrow $ 1 litre = $\dfrac{1}{1000}{{m}^{3}}$
Now, ${{m}^{3}}$ can be written as the product of three dimensions (length, breadth and height) each measured in meter, so we get,
$\Rightarrow $ 1 litre = $\dfrac{1}{1000}\times m\times m\times m$
We know that 1 m = 100 cm, so using this conversion we get,
$\Rightarrow $ 1 litre = $\dfrac{1}{1000}\times 100cm\times 100cm\times 100cm$
Cancelling the common factors we get,
$\Rightarrow $ 1 litre = 1000 $cm\times cm\times cm$
$\therefore $ 1 litre = 1000 $c{{m}^{3}}$
Hence, option (d) is the correct answer.

Note: You must remember the relationships between all the important units of measurement of not only volume but other physical quantities like length, area, time etc. There are generally two systems of units followed while writing the unit of a physical quantity, they are the S.I system of units and C.G.S system of units. Sometimes we are asked to convert one unit into the other and we need these conversion relations in such cases.