Question 25

The area of a circle with a diameter of 16 inches is 64π square inches.

To find the area of a circle, we use the formula A = πr². Given a diameter of 16 inches, the radius (r) is half of the diameter, which is 8 inches. Therefore, the area can be calculated as A = π(8)² = π(64) = 64π square inches.

A) 32π in squared

This option is incorrect because it implies that the radius used in the area calculation was too small. For a diameter of 16 inches, the correct radius is 8 inches, leading to an area much larger than 32π.

B) 64π in squared

This is the correct option as it accurately reflects the area calculated using the formula A = πr². With a radius of 8 inches, the area is 64π square inches, confirming this choice.

C) 256π in squared

This option is incorrect because it suggests that the area calculation used an incorrect radius, leading to an inflated result. The area cannot reach 256π with the given diameter of 16 inches.

D) 16π in squared

This option is also incorrect as it indicates a misunderstanding of the radius. The radius of 8 inches results in a much larger area than 16π, making this choice invalid.

Conclusion

The area of a circle with a diameter of 16 inches is correctly calculated to be 64π square inches, confirming that option B is the right answer. All other options underestimate or miscalculate the area due to incorrect interpretations of the radius derived from the diameter.