How to find the surface area, when the volume of a sphere is given.

A sphere is a set of points connected with one common point at equal distances.

Answer: The surface area of a sphere when the volume of a sphere is given is given by 4 × π × [3V / (4π)]^2/3

Let's look into the solution below

Explanation:

Given: 

Volume of a sphere = 4/3 × π × r³

Let's solve for r,

V = (4/3) × π × r³

⇒ r³ = 3V / 4π

⇒ r = [3V / (4π)]^1/3 ---------------- (1)

We know that,

The surface area of a sphere = 4 × π × r²

Using the value of r from (1) we get,

Surface Area = 4 × π × [{3V / (4π)}^1/3]²

                      =  4 × π × [3V / (4π)]^2/3

Hence, The surface area of the sphere = 4 × π × [3V / (4π)]^2/3