I Volume of a Frustum

  • Thread starter Jordan0332
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Jordan0332

The question is as follows:

Using all your Calculus knowledge, develop and justify, a formula for the rate of change of the heigh of a liquid in the cup, give:
- The machine pours the liquid at a constant rate - ie. flow rate is constant
- The shape of the cup is a "frustum", as given in the diagram
- No liquid is spilt during pouring

No values are given.

top radius = b
bottom radius = a
liquid radius = r

liquid height = h
frustum height = H
 
The equation to find the volume of frustum is ,
V=pi/3 * (a^2+b^2+ab)H
And you can use the similarity relations to get an equation relating the upper radius of the water column and the water height h.
substitute this relation in the V=qt relation (where q is the volume flow rate).
I hope you will do the differentiation part.
 

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