Two circular fields have radii in a 3:5 ratio. The first field's area is what percentage smaller than the second's?
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Answer: D. 64%
Explanation
Squaring the given radius ratio of three to five yields an area ratio of nine to twenty-five. The difference in area shares between the two circular fields is twenty-five minus nine, equaling sixteen units. Dividing sixteen by the second field area of twenty-five and multiplying by one hundred gives sixty-four percent smaller. Circular field areas scale quadratically based upon the square of their respective radii measurements. Percentage difference calculations compare a proportional deficit directly against the base value of the larger reference field. Ratio comparisons allow mathematicians to analyze relative sizes without needing actual physical unit measurements.
Option A assumes a linear relationship, incorrectly suggesting a fifty percent difference based on radius numbers. Option B underestimates the percentage deficit by failing to calculate the squared area ratios correctly. Option C represents a miscalculation of the proportional difference between the squared area values.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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