What is the area of a circle with a diameter of 16 inches in terms of pi (π)?

Rationale

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

The formula to calculate the area of a circle is πr², where r is the radius of the circle. Given that the diameter is 16 inches, the radius is half of that, or 8 inches. Substituting the radius into the formula, we get π*(8²), which equals 64π.

A (32π in squared) YOUR ANSWER

This choice is incorrect because it represents the area of a circle with a radius of approximately 5.66 inches. The diameter of such a circle would be approximately 11.31 inches, which is less than the given diameter of 16 inches.

B (64π in squared) CORRECT

This is the correct answer. The area of a circle with a diameter of 16 inches (and hence a radius of 8 inches) is determined by substituting the radius into the formula for the area of a circle, πr². This results in π*(8²) = 64π square inches.

C (256π in squared) YOUR ANSWER

This choice overestimates the area. It represents the area of a circle with a radius of 16 inches, not 8 inches. Remember, the diameter is 16 inches, so the radius is only half of that.

D (16π in squared) YOUR ANSWER

This choice underestimates the area. It represents the area of a circle with a radius of 4 inches. Since the diameter is 16 inches, the radius is 8 inches.

Conclusion

The formula for the area of a circle, πr², must be applied properly using the correct radius. Here, the diameter is given as 16 inches, which means the radius is 8 inches. By substituting the radius into the formula, we find that the area of a circle with a diameter of 16 inches is 64π square inches. Other choices either incorrectly calculated the radius or made errors in the calculation of the area.

What is the area of a circle with a diameter of 16 inches in terms of pi (π)?

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

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