Question

a circular serving tray has a diameter of 15 inches. what is its area? write your answer using π. show your work.

Explanation:

Step1: Find the radius

The radius \(r\) of a circle is half of the diameter \(d\). Given \(d = 15\) inches, so \(r=\frac{d}{2}=\frac{15}{2}\) inches.

Step2: Use the area formula

The area formula of a circle is \(A=\pi r^{2}\). Substitute \(r = \frac{15}{2}\) into the formula: \(A=\pi\times(\frac{15}{2})^{2}\).
Calculate \((\frac{15}{2})^{2}=\frac{15\times15}{2\times2}=\frac{225}{4}\). So \(A=\frac{225}{4}\pi\) square inches.

Answer:

The area of the circular serving tray is \(\frac{225}{4}\pi\) square inches.