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) = (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 .