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2021 JMPSC Sprint Problems/Problem 13

Revision as of 00:21, 11 July 2021 by Lamboreghini (talk | contribs) (→‎Solution)

Problem

Grace places a pencil in a cylindrical cup and is surprised to see that it fits diagonally. The pencil is $17$ units long and of negligible thickness. The cup is $8$ units tall. The volume of the cup can be written as $k \pi$ cubic units. Find $k$.

Sprint14.jpg

Solution

By the Pythagorean Theorem, we have that the diameter of the cylinder's base is 15 units long. Thus, the cylinder's base has radius $\frac{15}{2}$ units. Thus, the volume of the cylinder is $\left(\frac{15}{2}\right)^2\cdot8\pi=\boxed{450}\pi.$

~Lamboreghini

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