SOLUTION: A hollow glass bowl in the shape of a sphere of radius 15 in. is filled with water to a depth of 3 in. Find the volume of the water. If the water flows out through a small hole in

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Question 1181162: A hollow glass bowl in the shape of a sphere of radius 15 in. is filled with water to a depth of 3 in. Find the volume of the water. If the water flows out through a small hole in the bottom so that the level drops 2 in. How much water has escaped?
Answer by ikleyn(52847) About Me  (Show Source):
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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 = %282pi%2AR%5E2%2Ah%29%2F3 


     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 = %282%2A3.14159%2A15%5E2%5Eh%29%2F3 = 1413.716 cubic inches


Part (a) is solved.



Solve part (b) on your own, using the same formula.

Solved, answered, explained, instructed and completed.