Volume for a cone is:

V = pi * r^2 * h/3

We don't have enough information for the radius here. However, we can find the radius for the height in question using a proportion of similar triangles. We know the ratio of the height of the tank to the...

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Volume for a cone is:

V = pi * r^2 * h/3

We don't have enough information for the radius here. However, we can find the radius for the height in question using a proportion of similar triangles. We know the ratio of the height of the tank to the radius (diameter = 650 cm, so the radius is 325 cm). So:

325/600 = r/h

r = 325h/600 = 13h/24

So, plugging this in:

V = (pi/3) * (13/24)^2 * h^3

Taking the derivative of each side:

dV/dt = (pi/3)(13/24)^2 * (3h^2) * dh/dt

Plugging in the numbers:

dV/dt = (pi/3)(13/24)^2 * (3*350^2) * 24

dV/dt = 2,709,950.913 cubic cm / min

Now, dV/dt = V(in) - V(out). So

V(in) - 9500 = 2,709,950.913

V(in) = 2,719,450.913 cubic cm / min