SOLUTION: You are transplanting a fern from a pot in the shape of a rectangular prism into one in the shape of a cylinder. The height of the prism is triple its length. Its length is 8 cm gr

Algebra ->  Volume -> SOLUTION: You are transplanting a fern from a pot in the shape of a rectangular prism into one in the shape of a cylinder. The height of the prism is triple its length. Its length is 8 cm gr      Log On


   

Question 1151724: You are transplanting a fern from a pot in the shape of a rectangular prism into one in the shape of a cylinder. The height of the prism is triple its length. Its length is 8 cm greater than its width. The two pots have the same volume and the same height. What is the algebraic expression for the radius of the cylindrical pot?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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You are transplanting a fern from a pot in the shape of a rectangular prism into one in the shape of a cylinder.
The height of the prism is triple its length.
Its length is 8 cm greater than its width.
The two pots have the same volume and the same height.
What is the algebraic expression for the radius of the cylindrical pot?
:
let L = the length of the prism
then
(L-8) = the width
and
3L = the height of the prism and the height of the cylinder
:
Cylinder Vol = Prism vol
pi%2Ar%5E2%2A%283L%29+=+L%2A%28L-8%29%2A3L
pi%2Ar%5E2%2A%283L%29+=+3L%5E2%28L-8%29
pi%2Ar%5E2%2A%283L%29+=+3L%5E3-24L%5E2
simplify, divide thru by 3L
pi%2Ar%5E2+=+L%5E2-8L
r%5E2+=+%28L%5E2-8L%29%2Fpi
:
r = sqrt%28%28L%5E2-8L%29%2Fpi%29 is the radius