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Unformatted text preview: of the sphere, and x-axis points downwards (through the center of the sphere). The the cap is between x = 0 and x = h . The cross-section at r h level x is a circle, with radius p r 2-( r-x ) 2 . Thus the volume of the cap is V = Z h A ( x ) dx = Z h ( r 2-( r-x ) 2 ) dx = Z h (2 rx-x 2 ) dx = rx 2-x 3 3 # h = ( rh 2-h 3 3 ) 2...
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- Fall '06