Question

the radius of a semicircle is 8 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 of the circumference of a full circle) and the length of the diameter. The formula for the circumference of a full circle is \( C = 2\pi r \), so the length of the curved part is \( \frac{1}{2} \times 2\pi r=\pi r \). 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 \( r = 8 \) miles. Substitute \( r = 8 \) into the formula \( P=\pi r+2r \). We get \( P=\pi\times8 + 2\times8 \).

Step3: Calculate the value

First, calculate \( \pi\times8\approx3.14159\times8 = 25.13272 \) and \( 2\times8 = 16 \). Then add these two results together: \( 25.13272+16 = 41.13272 \).

Step4: Round to the nearest hundredth

Rounding \( 41.13272 \) to the nearest hundredth, we look at the thousandth place which is 2, so we keep the hundredth place as it is. So \( 41.13272\approx41.13 \).

Answer:

\( 41.13 \)