A circle has an area of 226.865 in squared. Assume pi=3.14. Find the radius of the circle.

Rationale

The radius of the circle is 8.50 in.

To find the radius of a circle given its area, we can use the formula \( A = \pi r^2 \). Rearranging this for the radius \( r \) gives us \( r = \sqrt{\frac{A}{\pi}} \). Substituting the area of 226.865 in² and π as 3.14 results in a radius of 8.50 inches.

A (15.05 m) YOUR ANSWER

This option is incorrect because it does not align with the calculated radius from the area provided. The conversion from inches to meters is not relevant here, as the calculations must remain consistent with the unit of measurement used for the area.

B (10.05 m) YOUR ANSWER

Similar to option A, this choice provides a radius that does not correspond to the calculated radius from the area of 226.865 in². Additionally, the radius derived from the area calculation is in inches, not meters.

C (8.50 in) CORRECT

This is the correct answer, as it accurately reflects the radius calculated from the area using the formula \( r = \sqrt{\frac{A}{\pi}} \). Upon substituting the values, we find that the radius equals 8.50 inches.

D (14.17 km) YOUR ANSWER

This option is incorrect since it presents a radius that is not derived from the area calculation and introduces a different unit of measurement (kilometers) that is not applicable here. The radius must remain in inches to maintain consistency with the given area.

Conclusion

The calculated radius of the circle based on the provided area of 226.865 in² is 8.50 inches, confirming that option C is the only correct choice. Other options either misrepresent the unit of measurement or do not match the calculations performed with the area formula.

A circle has an area of 226.865 in squared. Assume pi=3.14. Find the radius of the circle.

The radius of the circle is 8.50 in.

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