Difference between revisions of "2021 Fall AMC 12A Problems/Problem 9"
(→Solution 3) |
|||
Line 21: | Line 21: | ||
~MRENTHUSIASM | ~MRENTHUSIASM | ||
− | == Solution | + | == Solution 2 == |
The surface area is | The surface area is | ||
<cmath> | <cmath> | ||
Line 60: | Line 60: | ||
Therefore, the answer is <math>\boxed{\textbf{(E) }576}</math>. | Therefore, the answer is <math>\boxed{\textbf{(E) }576}</math>. | ||
~Steven Chen (www.professorchenedu.com) | ~Steven Chen (www.professorchenedu.com) | ||
− | |||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2021 Fall|ab=A|num-b=8|num-a=10}} | {{AMC12 box|year=2021 Fall|ab=A|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 20:40, 25 November 2021
Contents
Problem
A right rectangular prism whose surface area and volume are numerically equal has edge lengths and What is
Solution 1
The surface area of this right rectangular prism is
The volume of this right rectangular prism is
Equating the numerical values of the surface area and the volume, we have Dividing both sides by we get Recall that and so we rewrite as ~MRENTHUSIASM
Solution 2
The surface area is
The volume is
Hence,
Dividing both sides by , we get
Therefore, the answer is . ~Steven Chen (www.professorchenedu.com)
See Also
2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.