2008 AMC 12A Problems/Problem 8
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 and thus a surface area of .
A cube whose surface area is has a side of length and a volume of .
Alternatively, we can use the fact that the surface area of a cube is directly proportional to the square of its side length. Therefore, if the surface area of a cube increases by a factor of , its side length must increase by a factor of , meaning the new side length of the cube is . So, its volume is .
See Also
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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All AMC 12 Problems and Solutions |
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