Question

At the doctor's office, there is a scale that measures people's weight. The needle is 20 cm long, and it rotated 100° when Frank stepped on it. How far did the needle travel as it rotated?

Answer 1

Answer: 100(pi)/9

Explanation:

We use the equation (theta/360)(2)(pi)(r)

Theta = 100 (100 degrees of a 360 degree circle)

r = 10 (not 20 because that is the whole needle, we need half of 20 for the radius)

Plugging this in: 100/360 (2)(pi)(10)

2,000(pi)/360

Divide by 20 to simplify:
`(100\pi)/(9)`

Answer 2

Given:
length of the needle: 20 cm
angle 100°

We need to solve for the length of an arc to get the distance the needle has traveled.

Length of an Arc = n°/360° * 2πr
Length of an Arc = 100°/360° * 2 * 3.14 * 20cm
Length of an Arc = 0.28 * 125.6 cm
Length of an Arc = 35.17 cm