What is the length of an arc of 40° in a circle with an 8 inch radius?

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Answer 1 · 2015-10-17T06:14:55

Length = $5.587$ $5.587$ inches

Length of an Arc:

Length $= (d i a m e t e r) . π . \frac{∠}{360}$ $= (diameter).pi.(angle)/360$
diameter = $r a d i u s . 2$ $radius . 2$
diameter = 16 inches

Given $∠$ $angle$ = $40 d e g r e e s$ $40 degrees$

Length = $16.3 .142 . \frac{40}{360}$ $16.3.142. 40/360$
Length = $5.587$ $5.587$ inches

Can also be calculated using $s = r . θ$ $s = r.theta$

where r is measured in radians.

1 Degree = $\frac{π}{180}$ $pi / 180$ radians
40 Degrees = $\frac{π}{180} . 40$ $pi / 180 . 40$ radians