Question

What happens to the surface area of a sphere if the radius is doubled?b. What happens to the surface area of a sphere if the radius is tripled?

Answer 1

Given:

a) The radius is​ doubled.

b) The radius is​ tripled.

To find:

The changes to the surface area of a sphere

Step-by-step explanation:

Let us take the original radius as r.

The surface area of the original sphere is,

`A=4\pi r^2`

a) The new radius will be,

`R=2r`

So, the surface area of the sphere with the new radius is,

`\begin{gathered} A=4\pi R^2 \\ =4\pi(2r)^2 \\ =4\pi(4r^2) \\ A=4(4\pi r^2) \\ A=4* Surface\text{ area of old sphere} \end{gathered}`

Therefore, the surface area of a sphere becomes four times the original surface area if the radius is​ doubled.

b) The new radius will be,

`R=3r`

So, the surface area of the sphere with the new radius is,

`\begin{gathered} A=4\pi R^2 \\ =4\pi(3r)^2 \\ =4\pi(9r^2) \\ A=9(4\pi r^2) \\ A=9* Surface\text{ area of old sphere} \end{gathered}`

Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is​ tripled.