Question

the diameter of a circle is 5 centimeters. what is the area? give the exact answer in simplest form. square centimeters

Explanation:

Step1: Find the radius

The diameter \( d = 5 \) cm, and the radius \( r=\frac{d}{2}\). So \( r=\frac{5}{2} \) cm.

Step2: Use the area formula for a circle

The formula for the area of a circle is \( A = \pi r^{2} \). Substitute \( r=\frac{5}{2} \) into the formula: \( A=\pi\times(\frac{5}{2})^{2}=\pi\times\frac{25}{4}=\frac{25}{4}\pi \) square centimeters.

Answer:

\(\frac{25}{4}\pi\) square centimeters