Question

a. 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?

a. the surface area is multiplied by □.

Explanation:

Step1: Recall the formula for the surface area of a sphere

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\), where \(r\) is the radius of the sphere.

Step2: Calculate the surface area when the radius is doubled

Let the original radius be \(r\), so the original surface area \(S_{1}=4\pi r^{2}\). When the radius is doubled (\(r_{2} = 2r\)), the new surface area \(S_{2}=4\pi(2r)^{2}=4\pi\times4r^{2}=16\pi r^{2}\). Then \(\frac{S_{2}}{S_{1}}=\frac{16\pi r^{2}}{4\pi r^{2}} = 4\).

Answer:

\(4\)