Two cubes have volumes in a 729 : 1331 ratio. What is the ratio of their total surface areas?
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Answer: A. 81 : 121
Explanation
Taking the cube root of the given volume ratio of seven hundred twenty-nine to thirteen thirty-one gives the side length ratio. The cube roots of seven hundred twenty-nine and thirteen thirty-one are nine and eleven respectively. Squaring the side length ratio of nine to eleven produces a surface area ratio of eighty-one to one hundred twenty-one. Volume scales cubically with respect to linear dimensions, whereas surface area scales quadratically. Finding cube roots reverses the process of multiplying a linear dimension by itself three times to find volume. The total surface area of a cube is calculated by multiplying the square of a single side length by six.
Option B represents only the linear side length ratio rather than the squared surface area ratio. Option C repeats the original volume ratio without applying any geometric root or square operations. Option D provides an incorrect ratio that bears no mathematical relation to the cube volume numbers.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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