2008 AMC 12A Problems/Problem 8: Difference between revisions
New page: ==Problem== What is the volume of a cube whose surface area is twice that of a cube with volume 1? <math>\textbf{(A)} \sqrt{2} \qquad \textbf{(B)} 2 \qquad \textbf{(C)} 2\sqrt{2} \qqua... |
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==Problem== | ==Problem== | ||
What is the volume of a cube whose surface area is twice that of a cube with volume 1? | What is the [[volume]] of a [[cube]] whose [[surface area]] is twice that of a cube with volume 1? | ||
<math>\textbf{(A)} \sqrt{2} \qquad \textbf{(B)} 2 \qquad \textbf{(C)} 2\sqrt{2} \qquad \textbf{(D)} 4 \qquad \textbf{(E)} 8 </math> | <math>\textbf{(A)} \sqrt{2} \qquad \textbf{(B)} 2 \qquad \textbf{(C)} 2\sqrt{2} \qquad \textbf{(D)} 4 \qquad \textbf{(E)} 8 </math> | ||
Revision as of 17:28, 22 February 2008
Problem
What is the volume of a cube whose surface area is twice that of a cube with volume 1?
Solution
A cube with volume 
has a side of length ![$\sqrt[3]{1}=1$](http://latex.artofproblemsolving.com/3/c/6/3c65bfc5db8bea84fcd769f69191c1c492e6718f.png)
and thus a surface area of 
.
A cube whose surface area is 
has a side of length 
and a volume of 
.
See Also
| 2008 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 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 | |
