The lengths of the two circles are equal to 24.8 cm and 36.5 cm. Find the ratio of the areas of the circles bounded by these circles.
1. The circumference is calculated by the formula l = 2 * π * r (where l is the circumference, and r is its radius);
2. Calculate the radius of the first circle:
2 * π * r1 = 24.8;
r1 = 24.8 / 2 * π;
r1 = 12.4 / π;
3. Calculate the radius of the second circle:
2 * π * r2 = 36.5;
r2 = 36.5 / 2 * π;
r2 = 18.25 / π;
4. Calculate the area of the circles bounded by these circles by the formula S = π * r ^ 2:
S1 = π * (12.4 / π) ^ 2;
S1 = π * 153.76 / π ^ 2;
S1 = 153.76 / π;
S2 = π * (18.25 / π) ^ 2;
S2 = π * 333.0625 / π ^ 2;
S2 = 333.0625 / π;
5. Find the ratio of the areas of these circles:
S2 / S1 = 333.0625 / π / 153.76 / π = 333.0625 / 153.76 ≈ 2.17;
Answer: S2 / S1 ≈ 2.17.
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