Question

the area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6 pie. what is he measure of the angle subtended by the arc?

Answer 1

Area of the circle = pi * (radius)^2
78.5 = 3.14 * (radius)^2
radius = 5 cm
circumference of circle = 2*pi*radius = 2*3.14*5 = 10*pi cm

Now, we can get the subtended angle by the arc using the proportionality rule which states that:
(subtended angle / 360) = (arc length / circumference)
360 is a constant
arc length = 6 * pi
circumference = 10*pi cm

Substitute in the proportionality rule to get the angle as follows:
(angle / 360) = (6pi / 10pi)
(angle / 360) = 0.6
angle = 360 * 0.6 = 216 degrees