Filling containers and graphics

Calculus Level 2

The graphs shown represent the variation of the height in the water level of each container with respect to the time elapsed. Which graph does not correspond to any of the three vessels considering that the volumetric flow rate is constant?

Graph 1 Graph 2 Graph 3 Graph 4

Ronald Chén by Ronald Chén , 32, Guatemala

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2 solutions

Will van Noordt
Dec 30, 2017

The derivative of the water height represents the cross-sectional area of the container at that height. There is no container here with a cross-sectional area that is continuously increasing with height, as suggested by graph 4. Fun problem!

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Aniruddha Bagchi
Dec 31, 2017

Corresponding Graphs for Container A and B is pretty obvious (which is Graph 2 and Graph 3 respectively) as far as intuition is concerned but for Container C something non-intuitive happens. Watch Closely Watch Closely You can clearly see that rate of water height risen slows down as it reaches the top. So, Graph 4 is the odd one out .

Visit This Link : https://brilliant.org/wiki/related-rates-of-change/

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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