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| Math Central | Quandaries & Queries |
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Question from Shanto: In a jar of water, we kept a sphere with radius r. Then 75% of its volume went under water. Find out the distance of the top of the sphere from the surface of the water. |
Hi Shanto,
The key here is to know an expression for the volume of a spherical cap. In my diagram I have shaded the region below the water surface green. What you need is an expression for the volume of the blue region in terms of $r$ and $h.$
If you know some calculus you can find this volume using a volume of revolution technique. You can also look it up on the web.
Penny
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