# If the volume of a sphere doubles, what is the ratio of the surface area of the new, larger sphere to the old?

##### 1 Answer

Feb 23, 2016

The ratio of the surface area of the new, larger sphere to the old is

#### Explanation:

Let's start with two formulas - for surface area of a sphere

To double the volume, we have to increase the radius by multiplying it by

Indeed, let

Then the volume of a sphere with radius

With radius

The ratio of the new surface area to the old one equals to