March 15th, 2016, 10:26 AM  #11 
Math Team Joined: Jul 2011 From: Texas Posts: 3,033 Thanks: 1621 
x is variable ... it changes depending on the value of y your "green" length of x is when $y = 8$ ... $x = 10$ my "blue" length of x is when $y = 12$ ... $x = \sqrt{84}$ every point on the arc has a set of coordinates, (x,y), which change as you move on the arc ... look at the attached graph note at the bottom right corner of the bowl, x = 6 and y = 0 at the top right corner, x = 8 and y = 14 plug these coordinate values into the left side of the circle equation, $x^2+(y8 )^2$, and you'll still get $r^2=100$ 
March 15th, 2016, 12:27 PM  #12  
Member Joined: Sep 2014 From: UK Posts: 82 Thanks: 1  Quote:
 
March 15th, 2016, 12:37 PM  #13 
Math Team Joined: Jul 2011 From: Texas Posts: 3,033 Thanks: 1621 
the circle the problem speaks of is formed by the horizontal layer of water 12 cm from the bottom, not the center of the sphere ... the view in the sketch looks elliptical because it's viewed from the side


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