SOLUTION: A sphere has an area {{{64pi}}}, what is its volume?

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Question 97730: A sphere has an area 64pi, what is its volume?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A sphere has an area 64pi, what is its volume?


You need the formulas
A+=+4pi%2Ar%5E2 and V=%284%2F3%29pi%2Ar%5E3

We are given A=64pi, so we substitute in

A+=+4pi%2Ar%5E2
64pi+=+4pi%2Ar%5E2

Divide both sides by 4pi

%2864pi%29%2F%284pi%29+=+%284pi%2Ar%5E2%29%2F%284pi%29

16+=+r%5E2

Take positive square roots of both sides:

sqrt%2816%29=sqrt%28r%5E2%29

4+=+r

Substitute 4 for r in

V=%284%2F3%29pi%2Ar%5E3

V=%284%2F3%29pi%2A4%5E3

V=%284%2F3%29pi%2A64

V=%28256%2F3%29pi 

V=264.9409805

Edwin