A sector whose central angle measures #72°# has an area of #16.2pi# square feet. What is the radius of the circle?

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Answer 1 · 2016-05-05T03:25:06

The total centre angle of a circle is #360˚#. Thus, your sector measures #1/5# the total area of the circle.

The area of the total circle can therefore be found by multiplying #16.2pi# by #5#.

#16.2pi xx 5 = 81pi#

The formula for area of a circle is #a = r^2pi#. We are solving for r.

#81pi = r^2pi#

#(81pi)/pi = r^2#

#81 = r^2#

#9 = r#

The circle has a radius of 9 feet.

Hopefully this helps!