Boring a Bead
Boring a Bead
Suppose you have two wooden spheres with different radii. Holes are drilled through them to turn them into beads.
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If the length of the hole is the same in each of the spheres, show that the volume of material in each bead is the same.
You will probably need to know the volume of a piece that is sliced off a sphere like this:
[pic]
The sliced off piece is called a spherical cap. The formula for the volume of the spherical cap shown in the diagram is
[pic]
(You should check your understanding of this formula and see that it gives the right values for the volume when q = 0 as well as those values of the angle that describe a hemisphere and a sphere.)
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