Question

The area of the cross section of a sphere at the largest point is 100π square miles. what is the total surface area of this sphere? leave your answers in terms of π.

Answer 1

The cross-section of a sphere  is a circle . The  area of a circle can be calculated by the formula A= $\pi\r^{2}$ Where r is the radius of the circle.

Given :$\pir^{2} = 100\pi$

Solving for r we have:

$r^{2} = \frac{100\pi }{\pi}= 100$

Or r= 10.

The area of a sphere is calculated by the formula :

$SA = 4\pi R^{2}$

Substituting r value we have:

SA= $4\pi\ 10 ^{2} = 400\pi$

The total surface area of this sphere is 400π .