What is the area of a sector with a central angle of 5π6 radians and a radius of 5.6 ft? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. ft²

1 Answer
Jun 5, 2018

The area of the sector is 41.03 " square feet"

Explanation:

Given: r = 5.6 " ft, sector angle = " (5pi)/6

The area of a sector is the total area of the circle multiplied by the fraction of the circle that the sector takes up.

"Area " = pi r^2 * frac{theta}{2pi}

= pi (5.6)^2 * frac{(5pi)/6}{2pi}

= pi * (5.6)^2 * (5/12)

= pi * 31.36 * 5/12

(Round pi to 3.14)
= 3.14 * 31.36 * 5/12

= 41.03 " square feet"