1. ## Help with Radian Measure

A belt connects pulleys of diameter 2r and 2R with centres x apart. If r=20mm, R=120mm, and x=100*21/2mm, find the length L of the belt and the area of the region it encloses. Find the general expression for L in terms of r, R, x and Ø

3. ## Re: Help with Radian Measure

Yes, from that diagram I was able to work out that:
cosØ=100/100sqrt2
i.e.Ø=pi/4

But from that how do you work out the length of the belt?

4. ## Re: Help with Radian Measure

Originally Posted by KiaraG16
Yes, from that diagram I was able to work out that:
cosØ=100/100sqrt2
i.e.Ø=pi/4???? But from that how do you work out the length of the belt?
The non-blue part of the pulley's path is $\frac{3}{4}$ of the length circumference of the large circle.

The length of the linear blue part is $20+20=40$.
The length along the small circle is $\frac{1}{4}$ of its circumference.

In both cases the central angle is a right angle.

ADD these three lengths to get a total.