SOLUTION: Question: Which sector does not have an area of 3 pi. There are four possible answers given, A. central angle 135 degrees; radius 2 square root 2 B. central angle 80 degrees; radi

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Question 1159148: Question: Which sector does not have an area of 3 pi. There are four possible answers given, A. central angle 135 degrees; radius 2 square root 2
B. central angle 80 degrees; radius 3
C. central angle 67.5 degrees; radius 4
D. central angle 270 degrees; diameter 4
Thank you :)
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate the 4 areas and then you'll know.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For each case, find the area of the whole circle with the given radius. Then use the given central angle to find the fraction of a circle it represents. Multiply the whole area by that fraction to find the area of the sector.

A. central angle 135 degrees; radius 2 square root 2
The area of the whole circle is %28pi%29%282sqrt%282%29%29%5E2+=+8pi
135 degrees us 135/360 = 3/8 of the whole circle
area: %283%2F8%29%2A8pi+=+3pi

B. central angle 80 degrees; radius 3
The area of the whole circle is %28pi%29%283%29%5E2+=+9pi
80 degrees us 80/360 = 2/9 of the whole circle
area: %282%2F9%29%2A9pi+=+2pi

C. central angle 67.5 degrees; radius 4
The area of the whole circle is %28pi%29%284%29%5E2+=+16pi
67.5 degrees us 67.5/360 = 3/16 of the whole circle
area: %283%2F16%29%2A16pi+=+3pi

D. central angle 270 degrees; diameter 4
The area of the whole circle is %28pi%29%282%29%5E2+=+4pi
270 degrees us 270/360 = 3/4 of the whole circle
area: %283%2F4%29%2A4pi+=+3pi