A pulley system consists of a 10 inch wheel and another whose radius is unknown. A point on the rim of the wheel of unknown radius moves 450 inches when it revolves through an angle of 225 degrees. Find the angle the 10 inch wheel turns through

Answer 1

When you say "a 10 inch wheel" I will assume you have a radius of 10

arc length = rØ, where Ø is in radians
225° = 5π/4 radians

450 = r(5π/4)
r = 360/π inches = appr 114.59 inches (big wheel)

A point on the smaller wheel has to move 450 inches as well.
circumference = 20π
how many rotations ??
= 450/(20π) = 7.162 rotations
= appr 2578 °

Answer 2

Good work, but I interpret the wheel size as the diameter. If so, same steps apply, just adjusted for the smaller radius.