An arc with a measure of 190° has an arc length of 40\picentimeters. What is the radius of the circle on which the arc sits?

Question

An arc with a measure of 190° has an arc length of 40
`\pi`centimeters. What is the radius of the circle on which the arc sits?

Answer 1

37.9 cm

Explanation:

Arc length is:

s = 2πr (θ/360°)

where r is the radius and θ is the arc angle.

40π cm = 2πr (190°/360°)

20 cm = r (190°/360°)

r = 37.9 cm

Answer 2

Answer: the radius of the circle on which the arc sits is 3.8 cm

Explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

θ = 190 degrees

Length of arc = 40π centimeters

Therefore,

40π = 190/360 × 2 × π × r

Dividing both sides of the equation by π, it becomes

40 = 380r/360

380r = 40 × 360 = 1440

r = 1440/380

r = 3.8 to the nearest tenth