2001 AMC 10 Problems/Problem 21
Contents
Problem
A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter and altitude
, and the axes of the cylinder and cone coincide. Find the radius of the cylinder.
Solution 1
Let the diameter of the cylinder be . Examining the cross section of the cone and cylinder, we find two similar triangles. Hence,
which we solve to find
. Our answer is
.
Solution 2
:
We are asked to find the radius of the cylinder, or so we can look for similarity. We know that
and
, thus we have similarity between
and
by
similarity.
Therefore, we can create an equation to find the length of the desired side. We know that:
Plugging in yields:
Cross multiplying and simplifying gives:
.
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See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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