Question

the radius of a semicircle is 9 miles. what is the semicircles perimeter? round your answer to the nearest hundredth. miles

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 full circle is \( C = 2\pi r \), so half of that is \( \pi r \). The diameter \( d = 2r \). So the perimeter \( P \) of a semicircle is \( P=\pi r + 2r \).

Step2: Substitute the given radius into the formula

Given that the radius \( r = 9 \) miles. First, calculate the length of the curved part: \( \pi r=\pi\times9 = 9\pi \) miles. Then calculate the diameter: \( 2r=2\times9 = 18 \) miles. Now, find the perimeter by adding these two parts: \( P = 9\pi+ 18 \).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( 9\pi\approx9\times3.14159 = 28.27431 \) miles. Then add the diameter: \( 28.27431+ 18=46.27431 \) miles. Rounding to the nearest hundredth, we get \( 46.27 \) miles.

Answer:

\( 46.27 \)