The circumference of the circle is 72 cm, which means that the distance around the entire circle is 72 cm. The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and r is the radius of the circle.
We can rearrange this formula to solve for the radius:
r = C / 2π
Substituting the given value of the circumference, we get:
r = 72 / (2π)
r = 36 / π
To find the length of the minor arc AB, we need to know the measure of the central angle that intercepts it. If we assume that the circle has a total of 360 degrees, then the central angle that intercepts the minor arc is:
θ = (arc length / circumference) x 360°
The length of the minor arc AB is the same as the measure of the central angle that intercepts it, since the radius of the circle is 1. Therefore:
θ = AB
Substituting the known values, we get:
AB = (θ / 360°) x C
AB = (θ / 360°) x 72
AB = (θ / 360°) x 36 x 2
AB = (θ / 180°) x 36
Now we need to find the measure of the central angle that intercepts the minor arc AB. The entire circle has a central angle of 360 degrees, and the radius of the circle (which is also the radius of the minor arc AB) is:
r = 36 / π
Therefore, the length of the minor arc AB is:
AB = (θ / 180°) x 36
AB = (2 / π) x (36 / π) x 36
AB = 72π / π^2
AB = 72 / π
Using a calculator, we can approximate this value to two decimal places as:
AB ≈ 22.91
Therefore, the closest answer choice is A. 90 cm, which is approximately four times the actual length of the minor arc.