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.

Question

asked Feb 17, 2019 205k views

1 Answer

Anthony Sneed · Answer 1 · 2019-02-23T20:10:06+0000

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:

$r^(2) = (100\pi )/(\pi)=   100$

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 .