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 36π cm². the area of circle d is 324π cm². the area of the circle depends on the square of pi. the area of the circle depends on the central angle

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.

Step2: Analyze each option

• Option 1:

Since \(A=\pi r^{2}\), the area of the circle depends on the square of the radius. This is true.

• Option 2:

Given \(r = 18\) cm. If \(A=\pi r^{2}\), then \(A=\pi\times18^{2}=\pi\times324 = 324\pi\) \(cm^{2}\), not \(36\pi\) \(cm^{2}\). This is false.

• Option 3:

Given \(r = 18\) cm. Using \(A=\pi r^{2}\), \(A=\pi\times18^{2}=324\pi\) \(cm^{2}\). This is true.

• Option 4:

From \(A = \pi r^{2}\), the area depends on \(r^{2}\) (the square of the radius), not the square of \(\pi\). This is false.

• Option 5:

The formula \(A=\pi r^{2}\) does not involve the central angle. The area of a full - circle (central angle \(=360^{\circ}\)) is \(A=\pi r^{2}\), and for a sector with central angle \(\theta\) (in degrees) the area is \(A=\frac{\theta}{360}\pi r^{2}\). But for the area of the whole circle (\(\theta = 360^{\circ}\)), the area of the circle (as a whole) does not depend on the central angle. This is false.

Answer:

The area of the circle depends on the square of the radius; The area of circle D is \(324\pi\) \(cm^{2}\)