Geometry Geometry Math Forum

March 15th, 2016, 10:26 AM   #11
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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, $x^2+(y-8 )^2$, and you'll still get $r^2=100$
Attached Images
 circle_graph.jpg (20.9 KB, 8 views)

March 15th, 2016, 12:27 PM   #12
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Quote:
 Originally Posted by skeeter 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, $x^2+(y-8 )^2$, and you'll still get $r^2=100$
What I don't understand is not how x can vary but why would x be radius if radius goes from the centre of the circle. The definition of radius is that it goes from the centre of the circle to the circumference. Why, when working out surface area of a depth, would we take x to be r?

March 15th, 2016, 12:37 PM   #13
Math Team

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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
Attached Images
 FishBowl3.jpg (11.8 KB, 9 views)

 Tags bowl, circle, goldfish, height

,

### shows the cross section of a goldfish bowl

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