Answer
$29.36$ $inches$
Work Step by Step
$y$ $=$ $sin$ $($$\frac{\pi x}{7}$$)$
$\frac{2 \pi}{\frac{\pi}{7}}$ $=$ $14$$\pi$
$f(x)$ $=$ $sin$$($$\frac{\pi x}{7}$$)$
$y'$ $=$ $f'(x)$ $=$ $\frac{\pi cos(\frac{ \pi x}{7})}{7}$
$w$ $=$ $L$ $=$ $\int_{0}^{28}$ $\sqrt {1+[\frac{\pi cos (\frac{\pi x}{7})}{7}]^{2}}$$dx$
$w$ $\approx$ $29.36$ $inches$
