Question

assume the radius of a certain planet is 3180 km and the planet is a sphere. what is its surface area? the planets surface area is
(type an exact answer, using π)

Explanation:

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

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

Step2: Substitute the given radius into the formula

Given \(r = 3180\) km. Then \(S=4\pi\times(3180)^{2}\).
Calculate \((3180)^{2}=3180\times3180 = 10112400\).
So \(S = 4\pi\times10112400\).
Multiply \(4\times10112400=40449600\).

Answer:

The planet's surface area is \(40449600\pi\space km^{2}\)