Arc Length and Area of Sector│Please Help!

Question

Two connected gears are rotating. The smaller gear has a radius of 2.5 and the larger gear’s radius is 4.8. What is the angle through which the larger gear has rotated when the smaller gear has rotated 225 degrees?

Answer 1

225/360 = 75/120 = 25/40 = 5/8 of a turn for the small gear

its C = pid = 2pir = 2pi(2.5) = 5pi = circumferance

5/8 of 5pi = 25pi/8

big gear C = 2pi(4.8) = 9.6pi

25pi/8/9.6pi = 25/72 of a turn = 25/76.8 x 360=

= 117.1875 degree

turn when small gear turns 225 degrees

Answer 2

1. What is the circumference of the 2.3 gear?
2. How much of the circumference is covered in 225°?
3. What is the circumference of the 4.8 gear?
4. Divide #3 by #2.
5. Multiply 360° by #4.