Question

The surface area of two spheres are in the ratio of $9:25$. Then their volumes are in the ratio

• A. $81:625$
• B. $729:15625$
• C. $27:75$
• D. $27:125$

Answer 1

Answer: (D)

$27:125$

Given,

The ratio of surface area of two sphere

$=\frac{9}{25}$

We know that the surface area of the sphere

$=4\pi r^2$

So,

$\frac{4\pi r_1^2}{4\pi r_2^2}=\frac{9}{25}$

$\frac{r_1^2}{r_2^2}=\frac{9}{25}$

$\frac{r_1}{r_2}=\frac{3}{5}$

We know that the volume of the sphere

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

Therefore,

$=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}$

$=\frac{3^3}{5^3}$

$=\frac{27}{125}$

Hence, this is the answer.