1 Answer

Gregheo · Answer 1 · 2020-03-28T20:09:14+0000

Answer:

$(605)/(6)\pi \ cm^2$ or
$316.62\ cm^2$

Explanation:

step 1

Find the area of complete circle

The area of the circle is equal to

$A=\pi r^(2)$

we have

$r=11\ cm$

substitute

$A=\pi (11)^(2)$

$A=121\pi\ cm^2$

step 2

Find the area of the sector

Remember that the area of the complete circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of the region by a central angle of 300 degrees

$(121\pi)/(360^o)=(x)/(300^o)\\\\x=121\pi ((300^o)/(360^o))\\\\x=(36,300)/(360)\pi\ cm^2$

simplify

$x=(605)/(6)\pi \ cm^2$ ----> exact value

Find the approximate value

assume

$\pi =3.14$

$x=(605)/(6)(3.14)=316.62\ cm^2$

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