Question

The volume of a sphere is directly proportional to the cube of its radius. If the volumes of two spheres are in ratio $8:1$, what is the ratio of the radii of the spheres?

• A. $2:1$
• B. $1:2$
• C. $1:4$

Answer 1

The correct option is A $2:1$

Given: $\text{Volume of sphere}\propto {\text{(Radius)}}^3$

Now, from this, we can also say that the ratio of the volumes of two spheres will be proportional to the cubes of their radii.
$\Rightarrow \frac{\text{Volume of sphere 1}}{\text{Volume of sphere 2}}=\frac{{\text{(Radius of sphere 1)}}^3}{{\text{(Radius of sphere 2)}}^3}$

Given that the ratio of volumes of two spheres are in ratio $8:1$
$\therefore \frac{8}{1}=\frac{{\text{(Radius of sphere 1)}}^3}{{\text{(Radius of sphere 2)}}^3}$

$\Rightarrow \frac{\text{(Radius of sphere 1)}}{\text{(Radius of sphere 2)}}=(\frac{8}{1}{)}^{1/3}=\frac{2}{1}$