Question 943623: The circle below has a radius of 4 centimeters. What is the area of the shaded sector?
http://i.imgur.com/PcRGKBs.gif
I have tried to look up the formula for this but all I get is
area = 1/8 times pie times r^2
When I input it into a calculator, all I get is an extremely low number that can't be the answer to it, please assist me
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 45 / 360 = 1/8
that's true.
that would be equal to .125 which is the same as 1/8.
the area of the sector is 1/8 * pi * r^2 which is equal to 1/8 * pi * 16 which is equal to 2 * pi.
however, that is not the shaded area.
the shaded area is the rest of the circle, whose formula would be (360 - 45) / 360 * pi * 4^2 which simplifies to 7/8 * pi * 16 which simplifies to 14 * pi.
the whole area of the circle is equal to pi * 4^2 which is equal to 16 * pi.
1/8 * pi * 16 is equal to 2 * pi.
7/8 * pi * 16 is equal to 14 * pi.
add up the 1/8 and the 7/8 and you get the whole area of the circle.
you did get the area of a sector, only you got the area for the unshaded sector and not the shaded sector.
the shaded sector is what you needed to get.
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