Question 1189056
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A container in the shape of a sphere of radius 6cm is filled with water to depth of 10cm. 
(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 2cm, how much water escaped.
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<pre>
Use the formula for the volume of a spherical cap

    V = {{{(1/3)*pi*h^2*(3R-h)}}},


where R is the radius of the sphere and h is the height (= the depth) of the cap.


This formula works uninterruptedly in the entire diapason from h= 0 (empty container) to h= 2R (full container).


So, in case (a) you apply the formula at R= 6 cm and h= 10 cm

    V = {{{(1/3)*3.14159*10^2*(3*6-10)}}} = 837.76 cm^3.      <U>ANSWER</U>


I case (b), the final volume is

    V = {{{(1/3)*3.14159*8^2*(3*6-8)}}} = 670.21 cm^3.


The amount of water escaped is the difference  837.76 cm^3 - 670.21 cm^3 = 167.55 cm^3.    <U>ANSWER</U>
</pre>

Solved.


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For the formulas on the volume of a spherical cap see these Internet sources


https://mathworld.wolfram.com/SphericalCap.html


https://en.wikipedia.org/wiki/Spherical_cap