Answer:
[tex]\begin{gathered} 1.\text{ 62.8 inches} \\ 2.\text{ 10 inches} \end{gathered}[/tex]
Step-by-step explanation:
Since the rectangle is 8 inches by 10 inches, the circles are:
1. Use the equation of the perimeter of a circle, the radio of the circle is 1 inch, therefore:
*There are 14 half circles (7 full circles) and 4 of the 3/4 circles.
[tex]\begin{gathered} \text{ Total perimeter= }7\cdot(2\cdot\pi\cdot1)+4\cdot(\frac{3}{4}\cdot(2\cdot\pi\cdot1)) \\ \text{ Total perimeter=}20\pi \\ \text{ Total perimeter=62.8 inches} \end{gathered}[/tex]
2. Now, for the radius of the wireframe if you stretched out the perimeter would be 62.8 inches, substitute for the perimeter and solve for the radius:
[tex]\begin{gathered} 62.8=2\cdot\pi\cdot r \\ r=\frac{62.8}{2\pi} \\ r=10\text{ inches} \\ \text{ The radius would be 10 inches.} \end{gathered}[/tex]
