2017 AMC 12B Problems/Problem 14
Problem
An ice-cream novelty item consists of a cup in the shape of a 4-inch-tall frustum of a right circular cone, with a 2-inch-diameter base at the bottom and a 4-inch-diameter base at the top, packed solid with ice cream, together with a solid cone of ice cream of height 4 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?
Solution
We add up the volumes separately. The top cone has radius 2 and height 4 so we have
top cone = .
The frustum is made up by taking away a small cone of radius 1, height 4 from a large cone of radius 2, height 8, so
frustum = large cone - small cone = .
Adding, we get . Thus, the answer is E.
2017 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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