Question

the diameter of a semicircle is 30.6 kilometers. what is the semicircle’s perimeter? round your answer to the nearest hundredth. blank kilometers

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 diameter. The formula for the circumference of a circle is \( C = \pi d \), so half of that is \( \frac{1}{2}\pi d \). Then the perimeter \( P \) of the semicircle is \( P=\frac{1}{2}\pi d + d \).

Step2: Identify the given diameter

The diameter \( d = 30.6 \) kilometers.

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

First, calculate the length of the curved part: \( \frac{1}{2}\times\pi\times30.6 \). Let's compute that: \( \frac{1}{2}\times3.14159\times30.6 \approx 1.570795\times30.6 \approx 48.066327 \) kilometers. Then add the diameter: \( 48.066327+30.6 = 78.666327 \) kilometers.

Step4: Round to the nearest hundredth

Rounding \( 78.666327 \) to the nearest hundredth, we look at the thousandth place which is 6. Since \( 6\geq5 \), we round up the hundredth place: \( 78.67 \) kilometers.

Answer:

\( 78.67 \)