Question 999367: To carry their candy, Ariel, Ollie and Eden each have a bucket that looks like a pumpkin. It is completely spherical in shape with a straight slice across the top of the bucket that creates a circular opening for dropping in candy. If the radius of the bucket is 6 inches and the height, measured from the base of the bucket to the open top, is 9 inches, what is the area of the circular opening of the bucket, in square inches? Express your answer in terms of pi.
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! To carry their candy, Ariel, Ollie and Eden each have a bucket that looks like a pumpkin. It is completely spherical in shape with a straight slice across the top of the bucket that creates a circular opening for dropping in candy. If the radius of the bucket is 6 inches and the height, measured from the base of the bucket to the open top, is 9 inches, what is the area of the circular opening of the bucket, in square inches? Express your answer in terms of pi.
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Sketch the picture
From the center to the opening is 9-6 = 3 in
From the center to the edge of the opening is 6 in
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Draw that triangle including the radius of the opening.
radius = sqrt(6^2-3^2) = sqrt(36-9) = sqrt(27) in
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Ans: Area of opening = pi*radius^2 = 27pi sq in
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Cheers,
Stan H.
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