Difference between revisions of "2021 Fall AMC 10A Problems/Problem 3"
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== Solution == | == Solution == | ||
| + | A sphere with radius <math>2</math> has volume <math>\frac {32\pi}{3}</math>. A cube with side length <math>6</math> has volume <math>216</math>. If <math>\pi</math> was <math>3</math>, it would fit 6.75 times inside. Since <math>\pi</math> is approximately <math>5</math>% larger than <math>3</math>, it is safe to assume that the <math>3</math> balls of clay can fit <math>6</math> times inside. Therefore, our answer is <math>\boxed (D)6</math>. | ||
| + | |||
| + | ~Arcticturn | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2021 Fall|ab=A|num-b=2|num-a=4}} | {{AMC10 box|year=2021 Fall|ab=A|num-b=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:20, 22 November 2021
Problem
What is the maximum number of balls of clay of radius 
that can completely fit inside a cube of side length 
assuming the balls can be reshaped but not compressed before they are packed in the cube?
Solution
A sphere with radius has volume 
. A cube with side length has volume 
. If 
was 
, it would fit 6.75 times inside. Since is approximately 
% larger than , it is safe to assume that the balls of clay can fit times inside. Therefore, our answer is 
.
~Arcticturn
See Also
| 2021 Fall AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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