SOLUTION: Find the volume of a segment of a sphere,the radius of the base being 10.2 cms and the radius of sphere 12 cms
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Question 553694: Find the volume of a segment of a sphere,the radius of the base being 10.2 cms and the radius of sphere 12 cms Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! not sure if this is right, but, based on the reference http://en.wikipedia.org/wiki/Spherical_segment, the volume of a spherical segment is equal to:
pi*h/6 * (3r1^2 + 3r2^2 + h^2)
presumably y our segment extends from the middle of the sphere to a point above or below the middle of the sphere because you are only giving the base of the segment and the radius of the sphere which is presumed to the other base of the segment.
to solve for height, i took a cross-section of the sphere to form a right triangle with the radius of the sphere as the hypotenue and the base of the segment as one of the legs of the right triangle. the other leg ot the right triangle is the height of the segment which turned out to be sqrt(12^2 - 10.2^2) = 6.32139225.
i know had enough pieces to use the segment formula to get:
V(segment) = pi*h/6 * (3r1^2 + 3r2^2 + h^2) becomes:
V(segment) = pi*6.32139225/6*(3*10.2^2 + 3*12^2 + 6.32139225^2) which becomes:
V = 2595.205412
i confirmed that this segment plus the remaining segment from the top of the sphere to the top of this segment equaled half the volume of the sphere so i believe the formula is correct and that i probably did the calculations correctly.
if this is what you were asking then maybe this is the answer you want.
a picture of how i calculated the height is shown below:
