Two circles have circumferences of 264 meters and 352 meters. Find the difference in their areas.
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Answer: C. 4312 sq m
Explanation
Circumferences of two hundred sixty-four and three hundred fifty-two meters give radii of forty-two and fifty-six meters. Calculating the area of each circle using pi r squared gives respective circular surface areas. Subtracting the smaller circle area from the larger circle area yields an area difference of forty-three twelve square meters. Circle circumference equals two pi r, allowing direct calculation of the radius from boundary length. Area of a circle is proportional to the square of its radius multiplied by the mathematical constant pi. Difference in areas between two concentric or separate circles is found by subtracting their individual surface areas.
Urban planners calculate circular park and fountain surface areas to design surrounding landscaping features. Manufacturing industries determine circular sheet metal waste by finding differences between component areas. Mastering circle geometry formulas is essential for solving spatial and architectural word problems. Option A underestimates the area difference due to rounding approximations in the pi constant. Option B results from a minor arithmetic subtraction error in the final area calculation steps. Option D overshoots the correct area difference by miscalculating the squared radius values.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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