# How to find the surface area of a sphere with the volume?

Volume is the space inside the sphere while the surface area is the total outside area of the sphere.

## Answer: To calculate the surface area of the sphere with the volume, we use the formula: S = (π)^{1/3} × (6V)^{2/3}.

Let's go through the steps to understand the solution.

**Explanation:**

Given, volume of a sphere = 4 / 3 π r^{3}.

The surface area of a sphere can be calculated from the volume of the sphere, only if we know the radius of the sphere.

The surface area of the sphere = 4πr^{2}

From the formula of volume of a sphere, we can derive that, r^{3} = 3V/4π, or r = (3V/4π)^{1/3}.

Now, put the value of r in the formula of the surface area of the sphere.

4πr^{2}

= 4π(3V/4π)^{2/3}

= (4π)^{1/3} × (3V)^{2/3}

= (4)^{1/3} × (π)^{1/3} × 3^{2/3} × (V)^{2/3}

= (2)^{2/3} × 3^{2/3} × (π)^{1/3} × (V)^{2/3}

= (6)^{2/3} × (π)^{1/3} × (V)^{2/3}

= (π)^{1/3} × (6V)^{2/3}

### Thus, to calculate the surface area of the sphere with the volume, we use the formula S = (π)^{1/3} × (6V)^{2/3}.

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