Answered

The volume of a cylinder is 980 in cubed.

The height of the cylinder is 20 in. What is the radius of the cylinder?

Express your answer to the nearest hundredth.

Verified Answer :

apologiabiology

a cylinder is basically lots of circles stacked on top of each other so equation for volume of cylinder is (area of circle formula) times height

area of circle formula=pi times r^2
so volume of cylinder=pi times r^2 times height

volume=980 in
volume=pi times r^2 times height
height =20
subsitute
980=pi times r^2 times 20
divide both sides by 20
49=pi times r^2
divide both sides by pi
\(\frac{49}{pi}\)=r^2
square root both sides (remember that \(\sqrt{ \frac{x}{y} }= \frac{ \sqrt{x} }{ \sqrt{y} }\)) so

\(\frac{49}{pi}\)=\(\frac{ \sqrt{49} }{ \sqrt{pi}} = \frac{7}{ \sqrt{pi} }\)=r

try to make there be no radical (√) in the bottom so multiply top and bottom by \(\frac{ \sqrt{pi} }{ \sqrt{pi} }\)

\(\frac{7}{ \sqrt{pi} }\) times \(\frac{ \sqrt{pi} }{ \sqrt{pi} }\)=\(\frac{7 \sqrt{pi} }{pi}\)=radius≈(if aprox pi to 3.14)3.94933 in

the answer is (7√pi)/pi in or aprox 3.95 in


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