Given circle o with minor arc AB= 60 degrees and OA= 12. What is the area of sector AOB?

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Answer 1 · 2018-03-19T15:30:56

Area $= \frac{24}{5} π . . \leftarrow Exact answer$ $=24/5pi color(white)(..) larr" Exact answer"$

Area $= 15.08 {units}^{2}$ $=15.08" units"^2$ to 2 decimal places $\leftarrow Approximation$ $larr" Approximation"$

Tony B

Let the area of the sector be $a$ $a$

Circumference of a circle is $π D \Leftrightarrow 2 π r$ $piD hArr 2pir$

So the circumference of the whole circle is $2 π 12 = 24 π$ $2pi12=24pi$

But we only have $60^{o}$ $60^o$ worth of that circle

So as a fraction of the whole circle it is $\frac{60}{360} \equiv \frac{6}{30} \equiv \frac{1}{5}$ $60/360-=6/30-=1/5$

So the area of the sector is:

$a = \frac{1}{5} \times 24 π = \frac{24}{5} π . . \leftarrow Exact answer$ $a=1/5xx24pi=24/5pi color(white)(..) larr" Exact answer"$

$a=15.0796447......$

$a= 15.08" units"^2$ to 2 decimal places $larr" Approximate area"$