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

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:
$$$$

RELATED QUESTIONS
In the figure below, there are six circles and one rectangle. Each circle has a radius of (answered by Alan3354,mysteriousxone)

what is the volume of a rectangle package if the length is 55 cms breath is 40 cms and... (answered by waynest)

What calculator sequence will yield the volume of a sphere with radius? and Find the... (answered by zerosignal)

If the surface area and volume of a sphere have the same numerical value, find the radius (answered by Alan3354)

A sphere circumscribes a cube of side 4cm. a) What is the radius of the sphere? b) Find (answered by math_helper)

A sphere sits inside a cylinder and touches all sides. The radius of the sphere is 10... (answered by ikleyn)

A sphere is inscribed in a cone with radius 6 and height 8. Find the volume of the... (answered by venugopalramana)