Question

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.

Answer 1

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

`(49)/(pi)`=r^2
square root both sides (remember that
`\sqrt{ (x)/(y) }= ( √(x) )/( √(y) )`) so


`(49)/(pi)`=
`( √(49) )/( √(pi)) = (7)/( √(pi) )`=r

try to make there be no radical (√) in the bottom so multiply top and bottom by
`( √(pi) )/( √(pi) )`


`(7)/( √(pi) )` times
`( √(pi) )/( √(pi) )`=
`(7 √(pi) )/(pi)`=radius≈(if aprox pi to 3.14)3.94933 in

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