Question 1156175
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(1) What are we supposed to find?  rate of change of height: dh/dt<br>
(2) What are we given?  rate of change of volume: dV/dt<br>
So to solve the problem, we need to get the relationship between volume V and height h.<br>
{{{V = (1/3)(pi)(r^2)(h)}}}<br>
That gives us the volume in terms of r and h; so we need to get r in terms of h.<br>
The problem tells us d=h.  d = 2r; so r = (1/2)d = (1/2)h.<br>
Substitute in the volume formula:<br>
{{{V = (1/3)(pi)((1/2)h)^2(h) = (1/12)(pi)(h^3)}}}<br>
Now you are ready to take the derivative and solve the problem.<br>
{{{dV/dt = ((1/12)(pi)(3h^2))(dh/dt)}}}<br>
Plug in h=10 and the given value of dV/dt to solve for dh/dt....<br>