Difference between revisions of "2021 WSMO Speed Round Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | A square with side length of <math>4</math> units is rotated | + | 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== | ||
When a square is rotated about one of its sides, then it forms a cylinder. Thus, the answer is <math>4^3\pi\cdot\frac{90}{360}=16\pi.</math> Thus, the answer is <math>\boxed{16}.</math> | When a square is rotated about one of its sides, then it forms a cylinder. Thus, the answer is <math>4^3\pi\cdot\frac{90}{360}=16\pi.</math> Thus, the answer is <math>\boxed{16}.</math> | ||
| + | |||
| + | ~pinkpig | ||
Latest revision as of 13:23, 30 December 2021
Problem
A square with side length of 
units is rotated on one of its sides by 
. If the volume the square sweeps out can be expressed as 
, find 
.
Solution
When a square is rotated about one of its sides, then it forms a cylinder. Thus, the answer is 
Thus, the answer is 
~pinkpig
