Geometry and TrigonometryVery hardEdge ratio from a volume ratio
Geometry and Trigonometry practice question
The volume of cube A is 8 times the volume of cube B. The length of an edge of cube A is how many times the length of an edge of cube B?
Answer: 2
Volume scales with the CUBE of the edge. If the edge is multiplied by k, the volume is multiplied by k³. Here k³ = 8, so k = 2.
Common wrong answers
- If you answered 4
- 4 would be right if 8 were the ratio of AREAS (√8 is not 4 either); for volumes, take the cube root.
- If you answered 8
- 8 is the volume ratio, not the edge ratio; the edge ratio is its cube root.
- If you answered 2.67
- 2.67 is 8/3, dividing by 3 instead of taking the cube root.
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