A circle's area expands by 22 sq cm when its radius increases by 1 cm. What was the original radius_________?
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Answer: C. 3 cm
Explanation
The area of a circle is calculated by multiplying pi by the square of its radius. Expanding the radius by one unit creates a new area expression containing a linear term in r. Equating the area increase to twenty two allows solving the linear equation to find the original radius. Circle geometry dictates that area scales quadratically with respect to linear radius dimensions. The mathematical constant pi represents the ratio of a circle circumference to its diameter. Differential approximations can also estimate small changes in geometric areas and volumes.
Urban planners use circular growth models to estimate expanding coverage zones around city centers. Manufacturing processes rely on radius calculations to cut circular materials with minimal waste. Physics applications involve circular areas when determining electric and magnetic flux distributions. Option A suggests an overly large original radius that would produce a much greater area change. Option B represents a decimal approximation that fails to satisfy the exact algebraic increase. Option D incorrectly assumes a fractional radius value that contradicts the area expansion formula.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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