Question

which of the following statements about the area of a circle is true? choose the correct answer below. a. the area of a circle is π times the radius squared. b. the area of a circle is always larger than the area of a square where the diameter of the circle is the same as the length of the side of the square. c. the area of a circle is π times the diameter squared. d. the area of a circle is always a whole number.

Explanation:

• Option A: The formula for the area of a circle is \( A = \pi r^2 \), which means the area is \( \pi \) times the radius squared. This is correct.
• Option B: If the diameter of the circle (and side of the square) is \( d \), the area of the circle is \( \pi (\frac{d}{2})^2=\frac{\pi d^2}{4}\approx0.785d^2 \), and the area of the square is \( d^2 \). So the circle's area is smaller, so B is wrong.
• Option C: The area formula uses radius, not diameter squared. The diameter is \( 2r \), so \( \pi \times (\text{diameter})^2=\pi\times(2r)^2 = 4\pi r^2 \), which is not the area formula, so C is wrong.
• Option D: The area of a circle involves \( \pi \), so it's often a non - whole number (e.g., radius 1, area \( \pi\approx3.14 \)), so D is wrong.

Answer:

A. The area of a circle is \( \pi \) times the radius squared.