Question

If the radius of a sphere is half of the radius of another sphere, then their respective volumes are in the ratio

• A. $1:8$
• B. $2:1$
• C. $1:2$
• D. $8:1$

Answer 1

The correct option is A $1:8$

Let the radius of sphere be $r$ and radius of other sphere be $\frac{r}{2}.$

We know that the volume of the sphere

$=\frac{4}{3}\pi r^3$

Therefore,

$=\frac{\frac{4}{3}\pi {\left(\frac{r}{2}\right)}^3}{\frac{4}{3}\pi r^3}$

$=\frac{1}{8}\times \frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi r^3}$

$=\frac{1}{8}\times 1$

$=\frac{1}{8}$

Hence, the ratio is $1:8$