Question

Find the area of the shaded sector of the circle. Leave your answer in terms of pi.

Answer 1

Here you can see that the shaded area constitutes 3/4 of the whole circle. Thus, the area of the shaded sector is 3/4 of the area of the circle. How would you find that area? what is the area of the shaded sector?

Answer 2

You find the area by the usual thing which in this case makes
\[\pi 4 ^{2}\]
which leaves you with
\[16\pi \]

So... one sec!

Answer 3

Is it
\[12\]
with pi?

Answer 4

gotta have that pie. ;) In other words, yes, you must include pi in your response.

Answer 5

Yea! It wouldnt work when I tried to add it in the equation for some reason. That's right though?

Answer 6

Since you know how to use Equation Editor, present your answer as \[12 \pi ~sq~feet\]

Answer 7

Please note: It's worth learning how to find the area of a sector when the central angle (90 degrees in this case) isn't so "nice."

suppose the central angle were 37.5 degrees.

The aera of the corresponding sector would then be this fraction of the whole area:

37.5/360 (that is, 37.5 degrees out of a total of 360 degrees).

Answer 8

And you should know how to find the area of a sector when the central angle is measured in radians.

If the central angle were 1 rad., then the area of the corresponding sector would be
\[\frac{ 1~rad }{ 2 \pi ~rad }(area ~of~the ~whole ~circle)\]

Answer 9

ah, ok! these will definitely be useful, thanks!