Question

Xavier arranges a rope into three semi-circles to form the pattern shown

Answer 1

`L=(19)/(2)\pi\approx29.85in`

1) Notice that there are three semi-circles, so we have to use the formula of the Perimeter of the Circumference:

`s=\frac{2\pi\text{ r}}{2}=\pi r`

2) Notice that we have in the picture, the Diameter as 8" for two semicircles and 3" for the one in the middle. So we can write out the following expression:

`\begin{gathered} L=\pi r+\pi r+\pi r \\ L=4\pi+4\pi+(3)/(2)\pi \\ L=(19)/(2)\pi \end{gathered}`

Note the radius is half the diameter.

3) Hence, the length of the is 19π/2 (approximately 29.85 inches)