Difference between revisions of "2010 AMC 10A Problems/Problem 5"
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| − | 144 | + | == Problem 5 == |
| + | The area of a circle whose circumference is <math>24\pi</math> is <math>k\pi</math>. What is the value of <math>k</math>? | ||
| + | |||
| + | <math> | ||
| + | \mathrm{(A)}\ 6 | ||
| + | \qquad | ||
| + | \mathrm{(B)}\ 12 | ||
| + | \qquad | ||
| + | \mathrm{(C)}\ 24 | ||
| + | \qquad | ||
| + | \mathrm{(D)}\ 36 | ||
| + | \qquad | ||
| + | \mathrm{(E)}\ 144 | ||
| + | </math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | If the circumference of a circle is <math>24\pi</math>, the radius would be <math>12</math>. Since the area of a circle is <math>\pi r^2</math>, the area is <math>144\pi</math>. The answer is <math>\boxed{E}</math>. | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/C1VCk_9A2KE?t=290 | ||
| + | |||
| + | ~IceMatrix | ||
| + | |||
| + | == See Also == | ||
| + | |||
| + | {{AMC10 box|year=2010|ab=A|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Revision as of 06:19, 26 May 2020
Contents
Problem 5
The area of a circle whose circumference is 
is 
. What is the value of 
?
Solution
If the circumference of a circle is , the radius would be 
. Since the area of a circle is 
, the area is 
. The answer is 
.
Video Solution
https://youtu.be/C1VCk_9A2KE?t=290
~IceMatrix
See Also
| 2010 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
