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

Answer:

16 cm

Step-by-step explanation:

We have to first find the radius of the circle.

The area of a sector is given as:

$A = \frac{\alpha }{360} * \pi r^2$

where α = central angle of the sector = 120°

r = radius of the circle

Therefore:

$67 = \frac{120}{360} * \pi r^2\\\\\pi r^2 = \frac{360 * 67}{120}\\ \\r^2 = \frac{360 * 67}{120 * \pi}\\\\r^2 = 63.98\\\\r = \sqrt{63.98} = 8.0 cm$

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

D = 2 * 8 = 16 cm

The diameter of the circle is 16 cm