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2003 AMC 10B Problem 17

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2003 AMC 10B Problem 17AMC 10 Step by Step

Name: Date: September 13, 2026

Solid Geometry · difficulty 3 of 5 · about 2 min · position P16-20

An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies $75\%$ of the volume of the frozen ice cream. What is the ratio of the cone's height to its radius? (Note: a cone with radius $r$ and height $h$ has volume $\pi r^2 h / 3$ and a sphere with radius $r$ has volume $4 \pi r^3 / 3$ .)

A)
$2:1$
B)
$3:1$
C)
$4:1$
D)
$16:3$
E)
$6:1$

2003 AMC 10B Problem 17

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