Question

the diameter of a semicircle is 36 millimeters. what is the semicircles area? round your answer to the nearest hundredth. square millimeters

Explanation:

Step1: Find the radius

The diameter \( d = 36 \) mm, so the radius \( r=\frac{d}{2}=\frac{36}{2} = 18 \) mm.

Step2: Recall the area formula for a semicircle

The area of a full circle is \( A=\pi r^{2}\), so the area of a semicircle is \( A_{semicircle}=\frac{1}{2}\pi r^{2} \).

Step3: Substitute the radius into the formula

Substitute \( r = 18 \) into the formula: \( A_{semicircle}=\frac{1}{2}\times\pi\times(18)^{2} \).
First, calculate \( 18^{2}=324 \). Then, \( \frac{1}{2}\times\pi\times324 = 162\pi \).
Using \( \pi\approx3.14159 \), we get \( 162\times3.14159\approx508.93848 \).
Rounding to the nearest hundredth, we get \( 508.94 \).

Answer:

\( 508.94 \) square millimeters