The surface areas of two spheres are in the ratio 25 : 36. What is the ratio of their volumes?

Correct option is C

Given:
Surface area of two sphere ratio 25 : 36 .
Concept Used:
Surface Area of Sphere = $$4π r^2$$​​
Volume of Sphere = $$\frac{(4π )}{3} r^3$$​​
Solution:
Let the two Sphere are S1 and S2 .
Radius of  $$S_1 = r_1$$​ , Radius of $$S_2 = r_2,$$​​
Now, ratio of surface area of two spheres = $$\frac{(4π r_1^2)}{(4π r_2^2 )}$$​​
​$$\begin{aligned}&\frac{S_1}{S_2} = \frac{4\pi r_1^2}{4\pi r_2^2} \\&\frac{25}{36} = \frac{4\pi r_1^2}{4\pi r_2^2} \\&\frac{25}{36} = \frac{r_1^2}{r_2^2} \\&\sqrt{\frac{25}{36}} = \frac{r_1}{r_2} \\&\frac{r_1}{r_2} = \frac{5}{6}.\end{aligned}$$​​
Now,
Ratio of volume,
​$$\begin{aligned}&\frac{S_1}{S_2} = \frac{\frac{4\pi}{3} r_1^3}{\frac{4\pi}{3} r_2^3} \\&\frac{S_1}{S_2} = \frac{r_1^3}{r_2^3} \\&\frac{S_1}{S_2} = \frac{5^3}{6^3} \\&\frac{S_1}{S_2} = \frac{125}{216}.\end{aligned}$$​​