Question

# A wheel (r=3.5ft) turns to move a textile piece. How long the piece moved is if the wheel turns 130^circ?

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A wheel $$(r=3.5ft)$$ turns to move a textile piece. How long the piece moved is if the wheel turns $$\displaystyle{130}^{\circ}$$?

2021-02-24

Given:
$$r=3.5ft$$
$$\displaystyle\angle={130}^{\circ}$$
First, find $$\displaystyle\theta$$:
$$\displaystyle\theta=\angle\times{\left(\frac{\pi}{{180}^{\circ}}\right)}$$
$$\displaystyle\theta=\frac{{{130}\pi}}{{180}}$$
$$\displaystyle=\frac{{{13}\pi}}{{18}}$$
Use the formula:
$$\displaystyle{s}={r}\theta$$
Where s represents the length of the piece of cloth moved. Substitute:
$$\displaystyle{s}={3.5}\times\frac{{{13}\pi}}{{18}}$$
$$\displaystyle{s}\approx{8}$$ ft