SOLUTION: A child's play set comes with game pieces in the shapes of cones and cylinders. Each piece has the same height and each cone has twice the radius of each of the cylinders. What is

Algebra ->  Volume -> SOLUTION: A child's play set comes with game pieces in the shapes of cones and cylinders. Each piece has the same height and each cone has twice the radius of each of the cylinders. What is       Log On


   

Question 1138911: A child's play set comes with game pieces in the shapes of cones and cylinders. Each piece has the same height and each cone has twice the radius of each of the cylinders. What is the ratio of the volume of the cones to the volume of the cylinders?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let h and r be the height and radius of each cylinder. Then h and 2r are the height and radius of each cone.

The volume of each cylinder is %28pi%29%28r%5E2%29%28h%29.

The volume of each cone is %281%2F3%29%28pi%29%28%282r%29%5E2%29%28h%29+=+%284%2F3%29%28pi%29%28r%5E2%29%28h%29

The ratio of the volume of the cone to the volume of the cylinder is

%28%284%2F3%29%28pi%29%28r%5E2%29%28h%29%29%2F%28%28pi%29%28r%5E2%29%28h%29%29+=+4%2F3