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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ANSWERED
asked 2021-02-23

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

Answers (1)

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

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