SOLUTION: find the volume of the largest circular cone that can be cut out of a cube whose edge is 9cm.

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Question 424149: find the volume of the largest circular cone that can be cut out of a cube whose edge is 9cm.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:Since the edge of cube is 9 cm this will be the altitude of the cone.
The radius of circular cone will be 9:2=4.5 cm.
The volume of cone is given by formula: V=%281%2F3%29%2A%28pi%29%2AR%5E2%2AH, where R is the radius and H the altitude of cone. Since we are asked for the largest cone, its volume must be equal or less than the volume of cube. We write:
+%281%2F3%29%2A%28pi%29%2A%284.5%29%5E2%2A%289%29=
%281%2F3%29%2A%28pi%29%2A20.25%2A9=
V=60.75%28pi%29+cm%5E3