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?
:
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*r^2*(3L) = L*(L-8)*3L}}}
{{{pi*r^2*(3L) = 3L^2(L-8)}}}
{{{pi*r^2*(3L) = 3L^3-24L^2}}}
simplify, divide thru by 3L
{{{pi*r^2 = L^2-8L}}}
{{{r^2 = (L^2-8L)/pi}}}
:
r = {{{sqrt((L^2-8L)/pi)}}} is the radius