SOLUTION: A wooden cylinder is carved to form a cone that has the same base area and same height as the original cylinder. What fraction of the wooden cylinder is wasted? Give a reason.

Algebra ->  Volume -> SOLUTION: A wooden cylinder is carved to form a cone that has the same base area and same height as the original cylinder. What fraction of the wooden cylinder is wasted? Give a reason.      Log On


   

Question 1041490: A wooden cylinder is carved to form a cone that has the same base area and same height as the original cylinder. What fraction of the wooden cylinder is wasted? Give a reason.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The original cylinder has a volume of
V%5Bcyl%5D=pi%2AR%5E2%2AH.
The cone using the same base radius and height has a volume of,
V%5Bcone%5D=%28pi%2F3%29%2AR%5E2%2AH
So to go from cylinder to cone you need to remove this volume of wood,
V=V%5Bcyl%5D-V%5Bcone%5D
V=pi%2AR%5E2%2AH-%28pi%2F3%29R%5E2%2AH
V=%28%282pi%29%2F3%29R%5E2%2AH
V=%282%2F3%29V%5Bcyl%5D