Question

Find the length of an arc on a circle with radius 3 inches intercepted by a central angle of 30 degrees
Answered by oobleck
what a lot of work!
s = rθ = 3*π/6 = π/2 inches
Answered by GPT 3.5
The formula to find the length of an arc on a circle is given by:

Arc Length = (angle/360) * 2 * π * r

Where angle is the central angle in degrees, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, the radius is 3 inches and the central angle is 30 degrees.

Arc Length = (30/360) * 2 * π * 3
Arc Length = (1/12) * 2 * 3.14159 * 3
Arc Length = (1/12) * 2 * 3.14159 * 3
Arc Length = (1/12) * 2 * 3.14159 * 3
Arc Length = (1/12) * 2 * 3.14159 * 3
Arc Length = (1/12) * 6.28318 * 3
Arc Length = (1/12) * 18.8495
Arc Length = 1.5707 inches

Therefore, the length of the arc intercepted by a central angle of 30 degrees on a circle with a radius of 3 inches is approximately 1.5707 inches.
Answered by GPT 3.5
Apologies for the confusion caused by the excessive calculations in the previous explanation. You are correct, the formula for the length of an arc on a circle is s = rθ, where r is the radius and θ is the central angle in radians.

In this case, the radius is 3 inches and the central angle is 30 degrees. However, since the formula requires the angle to be in radians, we need to convert it.

To convert 30 degrees to radians, we use the formula radians = degrees * π / 180:

θ = 30 * π / 180
θ = π / 6 radians

Now we can use the formula s = rθ to find the length of the arc:

s = 3 * (π / 6)
s = π / 2 inches

Therefore, the length of the arc intercepted by a central angle of 30 degrees on a circle with a radius of 3 inches is π/2 inches.