SOLUTION: A cylinder 1 foot long and with a 6 inch radius is filled with water. A metal ball is dropped into the cylinder, and raises the water level two inches. Find the surface area of the

Algebra ->  Polygons -> SOLUTION: A cylinder 1 foot long and with a 6 inch radius is filled with water. A metal ball is dropped into the cylinder, and raises the water level two inches. Find the surface area of the      Log On


   

Question 475826: A cylinder 1 foot long and with a 6 inch radius is filled with water. A metal ball is dropped into the cylinder, and raises the water level two inches. Find the surface area of the sphere.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A cylinder 1 foot long and with a 6 inch radius is filled with water. A metal ball is dropped into the cylinder, and raises the water level two inches. Find the surface area of the sphere.
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The volume of the sphere = the water displaced = pi%2Ar%5E2%2Ah where h = the change in level.
V+=+pi%2A6%5E2%2A2+=+72pi cubic inches
For the sphere:
V+=+4%2Api%2Ar%5E3%2F3+=+72pi
r%5E3+=+72%2A3%2F4
r+=+root%283%2C54%29 inches
r =~ 3.77976 inches
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SA+=+4%2Api%2Ar%5E2
Area =~ 179.53 sq inches
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Note: The length of the cylinder is not relevant unless it's less than the diameter of the sphere.