Question

A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter $10$ and altitude $12,$ and the axes of the cylinder and cone coincide. Find the radius of the cylinder.

$\dfrac83$

$\dfrac{30}{11}$

$3$

$\dfrac{25}{8}$

$\dfrac72$

Answer: B

Concepts:similarity cone cylinder

Difficulty rating: 1680

Solution:

Take an axial cross-section. The cone has base radius $5$ and height $12;$ the cylinder appears as a rectangle of width $2r$ and height $2r.$

By similar triangles, $\dfrac{12-2r}{r}=\dfrac{12}{5},$ so $5(12-2r)=12r,$ giving $60=22r$ and $r=\dfrac{30}{11}.$

Thus, the correct answer is B.

2001 AMC 10 Problem 21

Answer: B

Difficulty rating: 1680

Solution:

Problem 21 in Other Years