If the surface areas of two spheres are in the ratio of 49 : 81, then find the ratio of their volumes.

Correct option is C

Given:
Ratio of surface area of two spheres = 49 : 81
Formula Used:
Volume of sphere =  $$\frac{4}{3} πr^3$$​​
Surface Area of sphere =  $$4πr^2$$​​
Solution:
Let the radius of spheres be x and y.
So, as per the question,
​$$4πx^2:4πy^2=49:81$$​​
→x :y= √(49:81)=7:9
Putting the radius in volume formula,
Ratio of volume = $$\frac{4}{3} π(7^3 ):\frac{4}{3} π(9^3)$$​​
Ratio of volume = $$7^3:9^3$$​​
Ratio of volume of spheres = 343 : 729.