Two circles have a radius ratio of 1:3. What is the ratio of their areas_________?
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Answer: C. 1:9
Explanation
Squaring the given radius ratio of 1 to 3 directly produces the area ratio of 1 to 9. The area of a circle scales quadratically with respect to any linear dimensional changes in its radius. Dividing the squared radius values yields the exact fractional proportion required for the circular areas. The area of a circular shape is calculated by multiplying the mathematical constant pi by the squared radius. Similar geometric figures exhibit area ratios that equal the square of their corresponding linear dimension ratios. Scaling any two-dimensional shape by a linear factor increases its total surface area by the square of that factor.
Option A incorrectly assumes that the ratio of areas remains identical to the linear ratio of radii. Option B incorrectly multiplies the radius ratio by two instead of squaring the linear scale factor. Option D uses an arbitrary numerical ratio that has no mathematical basis in circle geometry formulas.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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