What is the area, in square inches, of a circle with diameter 2 inches?

Rationale

The area of a circle with a diameter of 2 inches is 3.14 square inches.

To find the area of a circle, we use the formula A = πr². Given a diameter of 2 inches, the radius r is 1 inch. Substituting this value into the formula gives A = π(1)² = π, which is approximately 3.14 square inches.

A (6.28) YOUR ANSWER

This value represents the circumference of the circle rather than the area. The circumference can be calculated using the formula C = πd, where d is the diameter. With a diameter of 2 inches, the circumference is C = π(2) = 2π, which approximates to 6.28 inches.

B (3.14) CORRECT

This is the correct answer as it accurately represents the area of the circle. Using the area formula A = πr² and substituting r = 1 inch gives A = π(1)² = π, which is approximately 3.14 square inches.

C (1) YOUR ANSWER

This choice reflects the square of the radius but does not incorporate the π factor necessary for calculating the area of a circle. The area requires the multiplication of the radius squared by π, making this answer incorrect.

D (12.56) YOUR ANSWER

This value is twice the correct area. It results from using the formula for area incorrectly, as if doubling the correct area (A = 2πr²). The area of a circle with diameter 2 inches should not exceed 3.14 square inches.

Conclusion

The area of a circle is defined by the formula A = πr², where r is the radius. For a circle with a diameter of 2 inches, the radius is 1 inch, leading to an area of approximately 3.14 square inches. Other choices represent either the circumference or incorrect calculations, highlighting the importance of applying the correct formula.

What is the area, in square inches, of a circle with diameter 2 inches?

The area of a circle with a diameter of 2 inches is 3.14 square inches.

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