Question

the radius of a quarter circle is 8 meters. what is the quarter circles perimeter? round your answer to the nearest hundredth. meters

Explanation:

Step1: Recall the formula for the perimeter of a quarter - circle

The perimeter of a quarter - circle is composed of two radii and a quarter of the circumference of the whole circle. The formula for the circumference of a circle is \(C = 2\pi r\), so a quarter of the circumference is \(\frac{1}{4}\times2\pi r=\frac{\pi r}{2}\). The length of the two radii is \(2r\). So the perimeter \(P\) of a quarter - circle is \(P = 2r+\frac{\pi r}{2}\).

Step2: Substitute the value of \(r = 8\) into the formula

Given \(r = 8\) meters. First, calculate the length of the two radii: \(2r=2\times8 = 16\) meters. Then, calculate the length of the curved part: \(\frac{\pi r}{2}=\frac{\pi\times8}{2}=4\pi\) meters. Now, find the perimeter by adding these two parts together: \(P=16 + 4\pi\).

Step3: Calculate the numerical value

We know that \(\pi\approx3.14159\). So \(4\pi\approx4\times3.14159 = 12.56636\). Then \(P=16+12.56636 = 28.56636\).

Step4: Round to the nearest hundredth

Rounding \(28.56636\) to the nearest hundredth, we look at the thousandth place digit, which is \(6\). Since \(6\gt5\), we round up the hundredth place digit. So \(28.56636\approx28.57\).

Answer:

\(28.57\)