# Difference between revisions of "2021 JMPSC Sprint Problems/Problem 13"

## 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 $k$.

## 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

## Solution 2

The diameter is $15$. Therefore, $$\pi \left(\frac{15}{2}\right)^2 \cdot 8=450 \pi$$SO, $k=\boxed{450}$