Question

A circle has a radius of 8. Find the area of a sector of this circle that is intercepted by central angle measuring pi over 7

Answer 1

14.4 square units

Explanation:

Keep in mind that the area here is a fraction of the area of a full circle of radius 8.

(area of sector) = (fraction)(pi)(8)^2

The fraction is the given central angle (pi over 7) divided by 2pi:

pi 1

--------- * ----------- = 1/14

7 2pi

Multiply the formula (fraction)(pi)(8)^2 found above by this fraction:

area of sector = (1/14)(pi)(8)^2 = 14.4 square units