Question 26

The radius of the circle is 8.50 inches.

To find the radius of a circle given its area, we can use the formula for the area of a circle, \( A = \pi r^2 \). Given the area of 226.865 square inches and using \( \pi = 3.14 \), we can rearrange the formula to solve for the radius \( r \).

A) 15.05 m

This option is incorrect because it presents a radius that is significantly larger than what is calculated based on the given area. The conversion from area to radius using the formula does not support a radius of 15.05 meters.

B) 10.05 m

This option is also incorrect. Similar to option A, a radius of 10.05 meters would yield a much larger area than 226.865 square inches when calculated using the area formula, which does not fit the provided data.

C) 8.50 in

This is the correct option. Using the area formula \( A = \pi r^2 \), and substituting in the values, we find that \( r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{226.865}{3.14}} \approx 8.50 \) inches, which is consistent with the area provided.

D) 14.17 km

This option is incorrect as well. A radius of 14.17 kilometers would correspond to an area vastly exceeding 226.865 square inches. The units and magnitude do not match the context of the question.

Conclusion

The radius of 8.50 inches is accurately derived from the given area using the formula for the area of a circle. All other options either miscalculate the radius or present incorrect units and magnitudes, confirming that option C is the only valid solution based on the information provided.