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.

Printable View

- Sep 11th 2006, 11:52 AMHelpPleaseVolume 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.

- Sep 11th 2006, 12:27 PMThePerfectHacker
I would use integration consider a semi-circle.

.

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. - Sep 11th 2006, 12:29 PMgalactus
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. - Sep 11th 2006, 05:39 PMQuick
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