Two cubes have volumes in a 27:125 ratio. What is the ratio of their surface areas?
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Answer: C. 9:25
Explanation
The ratio of the volumes of two similar geometric cubes equals the cube of the ratio of their side lengths. A volume ratio of twenty seven to one25 implies that the side length ratio is three to five. The ratio of their surface areas equals the square of this side length ratio, resulting in nine to twenty five. Similar three dimensional shapes scale in linear dimensions, surface areas, and volumes according to distinct power rules. Cubing the side ratio three to five produces the volume ratio of twenty seven to one hundred twenty five. Squaring the linear scale factor yields the corresponding ratio for two dimensional surface areas of similar objects.
Six to twenty five incorrectly uses linear or mixed scaling factors instead of squaring the true side ratio. Three to five represents only the linear side length ratio rather than the requested surface area ratio. Sixteen to twenty five corresponds to an incorrect side length ratio of four to five instead of three to five.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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