The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Correct answer: D. 64%
- A. 50%
- B. 60%
- C. 40%
- D. 64%
Explanation
Areas of circles are proportional to the squares of their radii, so the area ratio is 3²:5² = 9:25. The first field is less by (25 - 9)/25 × 100% = 16/25 × 100% = 64%. The likely wrong choice is 60%, which compares the radii directly instead of their squared values.
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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.
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