Thread: Volume formula for cap of sphere

A hemispherical bowl of radius r contains water to a depth height h. Give a formula that you can use to measure the volume of the water in the bowl.

I would use integration consider a semi-circle.
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Let be the height i.e. distance from the endpoint on semicircle. Then what distance from the origon is .
Thus, the volume by revolving about the x-axis is given by,


Note: LaTeX (equation editor) is currectly disabled. In a few days these strange symbols I wrote down should turn into equations. If you know LaTeX you can follow this still.

There are various ways, but you could come up with a formula by rotating about the y-axis.




Try it with a sphere of radius 4, completely filled:



Check this against the formula for sphere volume.

This should help you understand what they're saying:
I realize it's of poor quality, but the things that were typed in latex are to the left, and the images they give are to the right