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.
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.
= (4π)1/3 × (3V)2/3
= (4)1/3 × (π)1/3 × 32/3 × (V)2/3
= (2)2/3 × 32/3 × (π)1/3 × (V)2/3
= (6)2/3 × (π)1/3 × (V)2/3
= (π)1/3 × (6V)2/3