Question

which statements are true regarding the area of circle d? select two options.□ the area of the circle depends on the square of the radius.□ the area of circle d is $36\pi \text{cm}^2$.□ the area of circle d is $324\pi \text{cm}^2$□ the area of the circle depends on the square of pi.□ the area of the circle depends on the central angle.

Explanation:

Step1: Recall circle area formula

The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius. This shows the area depends on the square of the radius.

Step2: Calculate area of circle D

The radius $r = 18$ cm. Substitute into the formula:
$A = \pi (18)^2 = 324\pi$ $\text{cm}^2$

Step3: Evaluate each statement

• Statement 1: True (matches the formula $A=\pi r^2$)
• Statement 2: False (calculated area is $324\pi$, not $36\pi$)
• Statement 3: True (matches the calculated area)
• Statement 4: False ($\pi$ is a constant, area does not depend on its square)
• Statement 5: False (central angle affects sector area, not full circle area)

Answer:

The area of the circle depends on the square of the radius.
The area of circle D is $324\pi \text{ cm}^2$