the radius of a circle O is 9 inches and the length of AB is 4pi inches. What is m<AOB?

Question

50
96
72
80

Answer 1

The length of an arc of a circle is given by the formula: arc length = radius * central angle.

In this case, the length of arc AB is given as 4π inches, and the radius of the circle is 9 inches.
So, we can write the equation as: 4π = 9 * central angle

Dividing both sides of the equation by 9, we get: π/2 = central angle

To convert the central angle from radians to degrees, we multiply by 180/π:
central angle = (π/2) * (180/π) = 90 degrees

The measure of angle AOB is equal to half the central angle, which is 90 degrees / 2 = 45 degrees.

Therefore, m<AOB = 45 degrees.

Answer 2

Not an option

Answer 3

Apologies for the mistake. Let's re-estimate the angle.
The length of the entire circumference of the circle is equal to 2πr, where r is the radius. In this case, the length of the entire circumference of the circle is 2π*9 = 18π inches.

The length of arc AB is given as 4π inches. To find the measure of angle AOB, we need to determine what fraction of the entire circumference arc AB represents.

Fraction of the circumference represented by arc AB = length of arc AB / entire circumference
= (4π) / (18π)
= 2/9

So, the measure of angle AOB is equal to this fraction multiplied by 360 degrees (since there are 360 degrees in a full circle):

measure of angle AOB = (2/9) * 360
= 80 degrees

Therefore, m<AOB = 80 degrees.