Question

the radius of a semicircle is 4 centimeters. what is the semicircles perimeter? round your answer to the nearest hundredth. centimeters

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 the 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 the semicircle is \( P=\pi r + 2r \).

Step2: Substitute the given radius \( r = 4 \) cm into the formula

First, calculate the curved part: \( \pi r=\pi\times4 = 4\pi \) cm. Then calculate the diameter: \( 2r = 2\times4=8 \) cm. Now add them together: \( P = 4\pi+8 \).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( 4\pi\approx4\times3.14159 = 12.56636 \). Then \( P\approx12.56636 + 8=20.56636 \).

Step4: Round to the nearest hundredth

Rounding \( 20.56636 \) to the nearest hundredth gives \( 20.57 \).

Answer:

\( 20.57 \) centimeters