Question

A stone which has a mass of 12 $g$ and a density of 3$gc{m^{ - 3}}$, is lowered into 20$c{m^3}$ of water in a measuring cylinder. What will be the new reading on the measuring cylinder?
A. 20 $c{m^3}$
B. 24 $c{m^3}$
C. 40 $c{m^3}$
D. 16 $c{m^3}$

Answer 1

Note – We will start solving this question by writing down the given information in the question. Then we will use the formula of density, i.e., Density = Mass / Volume, to find out the new reading on the measuring cylinder.
Formula used - Density = $\dfrac{\text{Mass}}{\text{Volume}}$

Complete step-by-step solution -
Given that,
Mass of the stone = 12$g$
Density of the stone = 3$gc{m^{ - 3}}$
And, the volume of the liquid in the measuring cylinder = 20$c{m^3}$
We know that,
The volume of the water increased in the measuring cylinder is equal to the volume of the stone.
Now, we have to calculate the volume of the stone which can be calculated by the formula of density, i.e.,
Density = Mass / Volume
$ \Rightarrow $Volume = Mass / Density
$ \Rightarrow $Volume $ = \dfrac{{12}}{3}$
$ \Rightarrow $Volume $ = 4c{m^3}$
The actual volume of liquid in the measuring cylinder is 20 $c{m^3}$.
So, the increase in volume will show a new reading = 20 $c{m^3}$+ 4 $c{m^3}$= 24 $c{m^3}$
Hence, the new reading on the measuring cylinder is 24 $c{m^3}$.

Note - Volume is the three-dimensional space occupied by a substance or enclosed by a surface. A Cylinder is a closed solid that has two parallel bases joined by a curved surface, at a fixed distance. While solving these kinds of questions, one should not have any doubts related to the formula, it must be clear which formula is suitable.