Question

the radius of a quarter circle is 13 kilometers. what is the quarter circle’s perimeter? round your answer to the nearest hundredth. kilometers submit

Explanation:

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

The perimeter of a quarter - circle (also known as the circumference of a quarter - circle plus the length of two radii) is given by the formula \(P=\frac{1}{4}(2\pi r)+2r\), where \(r\) is the radius of the circle. We can simplify this formula to \(P = \frac{\pi r}{2}+2r=r(\frac{\pi}{2} + 2)\).

Given that \(r = 13\) kilometers.

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

First, calculate \(\frac{\pi}{2}+2\). We know that \(\pi\approx3.14159\), so \(\frac{\pi}{2}\approx\frac{3.14159}{2}=1.570795\). Then \(\frac{\pi}{2}+2=1.570795 + 2=3.570795\).

Now, multiply this by \(r = 13\): \(P=13\times3.570795\).

Calculate \(13\times3.570795 = 46.420335\).

Step3: Round to the nearest hundredth

To round \(46.420335\) to the nearest hundredth, we look at the thousandth place. The digit in the thousandth place is \(0\), which is less than \(5\), so we keep the hundredth place digit as it is. So \(46.420335\approx46.42\).

Answer:

\(46.42\)