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# 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 × r^{3}

Let's solve for r,

V = (4/3) × π × r^{3}

⇒ r^{3} = 3V / 4π

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

We know that,

The surface area of a sphere = 4 × π × r^{2}

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}

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