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!

A sector whose central angle measures 72°72° has an area of 16.2pi16.2pi square feet. What is the radius of the circle?