Question

which statements are true regarding the area of circle d? choose two correct answers. the area of the circle depends on the central angle. the area of circle d is 36π cm². the area of circle d is 324π cm². the area of the circle depends on the square of pi.

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle. The area of a circle does not depend on the central angle (the formula for the area of a sector \(A=\frac{\theta}{360}\times\pi r^{2}\) depends on the central angle \(\theta\), but the area of the full - circle does not). Also, \(\pi\) is a constant (\(\pi\approx3.14\)), and the area of a circle does not depend on the square of \(\pi\).

Step2: Calculate the area of circle \(D\)

Given that the radius \(r = 18\space cm\). Substitute \(r = 18\) into the formula \(A=\pi r^{2}\). Then \(A=\pi\times(18)^{2}=\pi\times324 = 324\pi\space cm^{2}\)

Answer:

The area of circle \(D\) is \(324\pi\space cm^{2}\) (the third option) and the area of a circle depends on the radius (since \(A = \pi r^{2}\), and when we square the radius \(r\), it is equivalent to saying the area depends on the square of the radius. But among the given options, the correct ones are: The area of circle \(D\) is \(324\pi\space cm^{2}\) (the third boxed statement) and no other correct statements from the given options match the properties of the area of a circle formula. If we assume there was a mis - statement in the problem setup (maybe a typo in the options), but based on the formula \(A=\pi r^{2}\) with \(r = 18\), \(A=324\pi\) is correct. So the answer is the third option: The area of circle \(D\) is \(324\pi\space cm^{2}\)