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Difference between revisions of "2021 WSMO Speed Round Problems/Problem 2"

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==Problem==
 
==Problem==
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A square with side length of <math>4</math> units is rotated around one of its sides by <math>90^{\circ}</math>. If the volume the square sweeps out can be expressed as <math>m\pi</math>, find <math>m</math>.
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A square with side length of <math>4</math> units is rotated on one of its sides by <math>90^{\circ}</math>. If the volume the square sweeps out can be expressed as <math>m\pi</math>, find <math>m</math>.
  
 
==Solution==
 
==Solution==

Latest revision as of 13:23, 30 December 2021

Problem

A square with side length of $4$ units is rotated on one of its sides by $90^{\circ}$. If the volume the square sweeps out can be expressed as $m\pi$, find $m$.

Solution

When a square is rotated about one of its sides, then it forms a cylinder. Thus, the answer is $4^3\pi\cdot\frac{90}{360}=16\pi.$ Thus, the answer is $\boxed{16}.$

~pinkpig

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