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

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Answer 1 · 2018-06-05T19:35:27

The area of the sector is # 41.03 " square feet"#

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"#