Question

the diameter of a semicircle is 6 millimeters. what is the semicircles perimeter? round your answer to the nearest hundredth. millimeters

Explanation:

Step1: Find the radius

The diameter \( d = 6 \) mm, so the radius \( r=\frac{d}{2}=\frac{6}{2} = 3 \) mm.

Step2: Calculate the arc length

The formula for the circumference of a full circle is \( C = 2\pi r \), so the arc length of the semicircle is \( \frac{1}{2}\times2\pi r=\pi r \). Substituting \( r = 3 \), we get \( \pi\times3\approx3.1416\times3 = 9.4248 \) mm.

Step3: Add the diameter

The perimeter of the semicircle is the arc length plus the diameter. So \( P=9.4248 + 6=15.4248 \) mm.

Step4: Round to nearest hundredth

Rounding \( 15.4248 \) to the nearest hundredth gives \( 15.42 \) mm.

Answer:

\( 15.42 \)