SOLUTION: can someone help me please? I tried to solve it, but still confused. The shaded sectors of the two pulleys are similar (about 1/4 of each circle is shaded in diagram), so they

Algebra ->  Trigonometry-basics -> SOLUTION: can someone help me please? I tried to solve it, but still confused. The shaded sectors of the two pulleys are similar (about 1/4 of each circle is shaded in diagram), so they       Log On


   

Question 1075792: can someone help me please?
I tried to solve it, but still confused.
The shaded sectors of the two pulleys are similar (about 1/4 of each circle is shaded in diagram), so they will have the same central angle measure (do not assume it is 90 degree). Suppose that the shaded sector of the large pulley has an area of A1. Find an equation for A2, the shaded sector of the smaller pulley, in terms of d1(diameter of the larger pulley), d2(diameter of the smaller pulley), and A1.
Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let alpha be the percent of shading for both circles.
If it was fully shaded, alpha=1.
If it was not shaded at all, alpha=0
1.A%5B1%5D=alpha%2A%28%28pi%2AD%5B1%5D%5E2%29%2F4%29
2.A%5B2%5D=alpha%2A%28%28pi%2AD%5B2%5D%5E2%29%2F4%29
From eq. 1,
alpha=%284%2AA%5B1%5D%29%2F%28pi%2AD%5B1%5D%5E2%29
Substituting into eq. 2,

A%5B2%5D=A%5B1%5D%2A%28D%5B2%5D%5E2%2FD%5B1%5D%5E2%29%29
highlight%28A%5B2%5D=A%5B1%5D%2A%28D%5B2%5D%2FD%5B1%5D%29%5E2%29