Question

The density of cooking oil is $0.6gc{{m}^{3}}$. What is the mass of $18c{{m}^{3}}$ of the cooking oil?
A. 0.5g
B. 10.8g
C. 18.9g
D. 20g

Answer 1

Hint: Density of a body is the mass of the body in one unit volume of the body. If the mass of the body is uniformly distributed, then the density of the body is simply the ratio of the mass to the volume of the body.

Formula used:
$\rho =\dfrac{m}{V}$

Complete step by step answer:
Let us first understand what is meant by density of a body.
Density of a body is the mass of the body in one unit volume of the body. This means that if we take out a piece of one unit volume of the body, then its mass will be equal to the density of the body.
If the mass of the body is uniformly distributed, then the density of the body is simply the ratio of the mass to the volume of the body.
Suppose the mass of a body is m and the volume of the body is V, then its density is given as $\rho =\dfrac{m}{V}$ …. (i),
where $\rho $ is the density of the liquid.
 In the given case, the density of a cooking oil is given to be $0.6gc{{m}^{3}}$. It is asked to find the mass of the cooking oil of volume of $18c{{m}^{3}}$.
Therefore, $\rho =0.6gc{{m}^{3}}$ and $V=18c{{m}^{3}}$.
Substitute the values of in equation (i).
$\Rightarrow 18=\dfrac{m}{0.6}$
$\Rightarrow m=18(0.6)=10.8g$.
This means that the mass of the oil in the given volume is 10.8g.

So, the correct answer is “Option B”.

Note:
Note that the formula $\rho =\dfrac{m}{V}$ for the density of a body is valid only if the mass of the all mass of the body is uniformly distributed.
If the mass of the body is not constant and changes at every region, then the density of the body is not the same at all the points.
The ratio of two extensive properties of the same object or system is an intensive property.