There are two circular models, one with radius 7 inches and another is radius 6.5 inches
Since the angles are in degrees, let us convert the angles from degree to radian.
[tex]\begin{gathered} 45^o=\frac{\pi}{4} \\ 40^o=\frac{2\pi}{9} \end{gathered}[/tex]the length of the curve section with radius 7 inches is
[tex]\begin{gathered} A=\frac{\pi}{4}\times7 \\ =5.497 \end{gathered}[/tex]the length of the curve section with radius 6.5 inches is
[tex]\begin{gathered} B=\frac{2\pi}{9}\times6.5 \\ =4.538 \end{gathered}[/tex]So, the total length is
[tex]\begin{gathered} L=5.497+4.538 \\ =10.035 \\ \approx10.0\text{ (rounded off to the nearest tenth)} \end{gathered}[/tex]Hence, the correct option is (c)