Freeflows

Ice Cream Cone Ratio

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 $.)

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$\frac{a}{b}$
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0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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