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 r³.

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 = 4πr²

From the formula of volume of a sphere, we can derive that, r³ = 3V/4π, or r = (3V/4π)^1/3.

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

4πr²

= 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.