SOLUTION: A sphere of radius x is melted and its volume is divided into two equal parts. One part is cast into a cylinder of height 10 cm, and second a cone of the same height. The ratio

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Question 1097092: A sphere of radius x is melted and its volume
is divided into two equal parts. One part is
cast into a cylinder of height 10 cm, and
second a cone of the same height. The ratio
of the cylinder radius to the cone radius is
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!

If the heights of the cylinder and cone are same and the volumes are the same, then the cone will have the larger radius. So let r (little r) be the radius of the cylinder, and let R (big r) be the radius of the cone.

The volume of the cone is
%281%2F3%29%28pi%29%28R%5E2%29%2810%29

The volume of the cylinder is
%28pi%29%28r%5E2%29%2810%29

Since the volumes are equal,
%281%2F3%29%28pi%29%28R%5E2%29%2810%29+=+%28pi%29%28r%5E2%29%2810%29
%281%2F3%29R%5E2+=+r%5E2
1%2F3+=+r%5E2%2FR%5E2
sqrt%281%2F3%29+=+r%2FR

The ratio of the cylinder radius to the cone radius is
sqrt%281%2F3%29+=+1%2Fsqrt%283%29+=+sqrt%283%29%2F3