MathDB
We All Scream For Ice Cream

Source: 2017 AMC 12B #14

February 16, 2017
AMCAMC 12AMC 12 Bgeometry3D geometryfrustum

Problem Statement

An ice-cream novelty item consists of a cup in the shape of a 44-inch-tall frustum of a right circular cone, with a 22-inch-diameter base at the bottom and a 44-inch-diameter base at the top, packed solid with ice cream, together with a solid cone of ice cream of height 44 inches, whose base, at the bottom, is the top base of the frustum. What is the total volume of the ice cream, in cubic inches?
<spanclass=latexbold>(A)</span> 8π<spanclass=latexbold>(B)</span> 28π3<spanclass=latexbold>(C)</span> 12π<spanclass=latexbold>(D)</span> 14π<spanclass=latexbold>(E)</span> 44π3<span class='latex-bold'>(A)</span>\ 8\pi\qquad<span class='latex-bold'>(B)</span>\ \frac{28\pi}{3}\qquad<span class='latex-bold'>(C)</span>\ 12\pi\qquad<span class='latex-bold'>(D)</span>\ 14\pi\qquad<span class='latex-bold'>(E)</span>\ \frac{44\pi}{3}