Question

The diameter of a circle is 8 centimeters. a central angle of the circle of the circle intercepts an arc of 12 centimeters. what is the radian measure of the angle?

Answer 1

The radian measure of the angle is 1.5 radians.

Step-by-step explanation:

To find the radian measure of the angle, we need to determine the length of the arc intercepted by the angle. We know that the diameter of the circle is 8 centimeters, so the radius is half of that, which is 4 centimeters. The circumference of the circle is given by the formula C = 2πr, where r is the radius.

In this case, the arc length intercepted by the angle is 12 centimeters. We can use the formula for the circumference to find the radian measure of the angle.

C = 2πr

12 = 2π(4)

12 = 8π

Dividing both sides of the equation by 8, we get:

π = 1.5 radians

Answer 2

The diameter of the circle is 8 cm, so the radius of the circle is R=4cm.

The Circumference of the circle is 2πR=8π cm

Let the measure of the central angle be x.

the arc that angle x intercepts is 8/8π=1/π of the circumference. (approximately 1/3.14 or 1 third, so x will be 1 third of 360°=2π rad)

this is the ratio that x forms to the full angle 2π rad


`(x)/(2 \pi ) = (1)/( \pi )`

x= 2 rad.

Answer: 2 rad