Question 383221
We have

{{{V = (pi/3)(hr^2)}}} (separating all the constants)

h and r are both functions in terms of time, t. We can take dV/dt by the product rule:

{{{dV/dt = (pi/3)((dh/dt)r^2 + h*(2r)*(dr/dt))}}}

At this instant, we have {{{dh/dt = 3 cm/s}}}, {{{h = 15 cm}}}, {{{dr/dt = 2 cm/s}}}, and {{{r = 5 cm}}}. Substituting all of the known variables in, we obtain

{{{dV/dt = (pi/3)(75 cm^3/s + 200 cm^3/s) = ((275*pi)/3) (cm^3/s)}}}