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