Answer:
- linear dimensions: 2 : 7
- areas: 4 : 49
- volumes: 8 : 343
Explanation:
You want the area and volume ratios when two figures have a similarity ratio of 2 : 7.
Area
The ratio of areas is the square of the similarity ratio:
2² : 7² = 4 : 49
Volume
The ratio of volumes is the cube of the similarity ratio:
2³ : 7³ = 8 : 343
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Additional comment
It can help to think about the units of area and volume. For linear dimensions in inches, area dimensions are in square inches, and volume dimensions are cubic inches. Any ratio of inches will be squared when those inch dimensions are used for area, and will be cubed when volume is computed.
side length of a square or cube: smaller: 2", larger: 7"
area of the square: smaller: 2² in², larger: 7² in² or 4 in² and 49 in²
volume of the cube: smaller: 2³ in³, larger: 7³ in³ or 8 in³ and 343 in³
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