Radian and Degree Measure

Question

Find the area of the sector of a circle of radius 15⁢cm with a central angle of 3π4. Round the solution to two decimal places.

Answer 1

sector area = half radians times radius squared

A = .5theta(r^2) with theta measured in radians, not degrees

radius = 15 cm

theta = 3pi/4 radians

A = (1/2)(3pi/4)(15^2) = (3pi/8)(225) = 675pi/8 = 84.375pi square centimeters

rounded to 2 decimals = 84.38pi cm^2

but you probably want something slightly different

= 84.375(3.14)

= about 265.07 cm^2 rounded to 2 decimals

Answer 2

The area of a sector based on the central angle is determined by the fraction that the central angle is of 2π times the area of the circle. In this case:

A = πr² (3π/4)/2π = (3/8)πr²

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