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A hollow glass bowl in the shape of a sphere of radius 15 in. is filled with water to a depth of 3 in.
(a) Find the volume of the water.
(b) If the water flows out through a small hole in the bottom so that the level drops 2 in,
How much water has escaped?
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(a) You have spherical segment; the radius of the sphere is R = 15 in;
the height of the cap (which is, in fact, the depth of the water) is h = 3 in.
Use a formula for the spherical segment volume
V =
As a reference, see these web-sites
https://www.math24.net/sphere#:~:text=V%3D%20%CF%80h(3r,base%20of%20the%20spherical%20cap.
https://en.wikipedia.org/wiki/Spherical_cap
Substitute the given data into the formula and calculate
V = = 1413.716 cubic inches
Part (a) is solved.
Solve part (b) on your own, using the same formula.
Solved, answered, explained, instructed and completed.