Question

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

Answer 1

The length of the intercepted arc can be calculated through the equation,

A = (θ/2π)(2πr)

where r is the radius. We are given that the value of diameter is 8 cm. Radius can be calculated by dividing the given diameter by 2.

radius = 8 cm/2 = 4 cm

Substituting the known values to the equation above,

12 cm = (θ/2π)(2π)(4 cm)

The value of θ from the equation is 3.

Answer: 3 radians