Math CentralQuandaries & Queries


Question from Barbara, a student:

Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s.
How fast is the volume of the cone increasing when r = 10 and h = 20?

Hi Barbara,

The volume of a cone of radius r cm and height h cm is given by

V = 1/3 π r2 h.

V, r and h are all functions of time and you are told that dr/dt = dh/dt = 2 cm/s. What you want is dV/dt when r = 10 cm and h = 20 cm.

Differentiate V = 1/3 π r2 h implicitly with respect to t and you will see that you know the value of each of the variables except dV/dt. Solve for dV/dt.


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