Question

I was supposed to determine the length of the winding path through the circle.

my answer is

`12.56 \: in {}^(2)`
Is this correct?​

Answer 1

Check the picture below.

the idea being, the winding path is made out of semi-circles, each semi-circle has a diameter of 3, as you see there in the picture.

now, if we could just take two semi-circles, we'd have a full circle, with a diameter of 3, so from all 4 semi-circles we can actually get two full circles, as you see there, and the circumference of those two full circles, is the length of the winding path.

`\bf \textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=3 \end{cases}\implies C=3\pi \qquad \stackrel{\textit{two circles added together}}{3\pi +3\pi \implies 6\pi ~~\approx~~18.85}`