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2022 SSMO Accuracy Round Problems/Problem 2

Revision as of 12:02, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Consider a cone with radius <math>5</math> and height <math>12</math>, and a point <math>P</math> in the same plane as the base of the cone, but a distance of <mat...")
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Problem

Consider a cone with radius $5$ and height $12$, and a point $P$ in the same plane as the base of the cone, but a distance of $10$ from the center of the base of the cone. We rotate the cone $360^{\circ}$ about $P$ such that the plane that the base of the cone lies on stays the same. The volume of the region that the cone sweeps out can be expressed as $m\pi$. Find $m$.

Solution

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