Question

For what radius of a sphere is its surface area and volume the same value? ​

Answer 1

Surface area of sphere = 4πr²

Volume of sphere = (4/3) πr³

Let these be same(numerically) for radius = R.

→ Surface area = volume

4πr² = (4/3) πr³

r² = r³/3

3r² =r³

3r² - r³ = 0

r² (3-r)=0

r² = 0

r=0

Answer 2

Surface area of sphere = 4πr²

Volume of sphere = (4/3) πr³

Let these be same(numerically) for radius = R.

→ Surface area = volume

4πr² = (4/3) πr³

r² = r³/3

3r² =r³

3r² - r³ = 0

r² (3-r)=0

r² = 0

r=0