Question

a 120 degree sector of a circle has an area of 67 square centimeters. to the nearest centimeter, what is the diameter of the circle?

Answer 1

16 cm

Explanation:

We have to first find the radius of the circle.

The area of a sector is given as:

`A = (\alpha )/(360) * \pi r^2`

where α = central angle of the sector = 120°

r = radius of the circle

Therefore:

`67 = (120)/(360) * \pi r^2\\\\\pi r^2 = (360 * 67)/(120)\\ \\r^2 = (360 * 67)/(120 * \pi)\\\\r^2 = 63.98\\\\r = √(63.98) = 8.0 cm`

The diameter of a circle is twice its radius, therefore:

D = 2 * 8 = 16 cm

The diameter of the circle is 16 cm