Question

the diameter of a semicircle is 16 miles. what is the semicircles perimeter? round your answer to the nearest hundredth. miles submit

Explanation:

Step1: Recall the formula for the perimeter of a semicircle.

The perimeter of a semicircle is the sum of the length of the curved part (half the circumference of the full circle) and the length of the diameter. The formula for the circumference of a circle is \( C = \pi d \), so half of that is \( \frac{1}{2}\pi d \). Then we add the diameter \( d \) to get the perimeter \( P \) of the semicircle: \( P=\frac{1}{2}\pi d + d \).

Step2: Identify the given diameter.

We are given that the diameter \( d = 16 \) miles.

Step3: Substitute the value of \( d \) into the formula.

First, calculate the length of the curved part: \( \frac{1}{2}\pi d=\frac{1}{2}\times\pi\times16 = 8\pi \) miles. Then add the diameter: \( P = 8\pi+ 16 \).

Step4: Calculate the numerical value.

Using \( \pi\approx3.14159 \), we have \( 8\pi\approx8\times3.14159 = 25.13272 \). Then add 16: \( 25.13272 + 16 = 41.13272 \).

Step5: Round to the nearest hundredth.

Rounding \( 41.13272 \) to the nearest hundredth gives \( 41.13 \).

Answer:

\( 41.13 \)