Question

the diameter of a semicircle is 16 millimeters. what is the semicircles area? round your answer to the nearest hundredth. square millimeters

Explanation:

Step1: Find the radius

The diameter \( d = 16 \) mm, so the radius \( r=\frac{d}{2}=\frac{16}{2} = 8 \) 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 \( r = 8 \) into the formula: \( A_{semicircle}=\frac{1}{2}\times\pi\times8^{2}\).
First, calculate \( 8^{2}=64 \). Then, \( \frac{1}{2}\times\pi\times64 = 32\pi \).
Using \( \pi\approx3.14159 \), we get \( 32\times3.14159\approx100.53088 \).

Step4: Round to the nearest hundredth

Rounding \( 100.53088 \) to the nearest hundredth gives \( 100.53 \).

Answer:

\( 100.53 \) square millimeters