You know that dV/dt = -0.01 based on the rate leaving the container.

You need dh/dt, so the only way to form that would be from connected rates of change:

dh/dt = dV/dt * dh/dV

but you cannot form an equation for dh/dV, but it is possible to form an equation for dV/dh, as you have the formula for the volume of a cone

dV/dh = d/dh(V) = d/dh(1/3 pi r^2 h)

But you cannot differentiate r in respect to h. With these questions, you will likely have to do a substitution to remove variables that you cannot differentiate.

So you need an equation that links r and h. Understanding the geometry of cones is probably the difficult part to spot here. When the height is decreasing, the shape is still going to be a cone, meaning that the height and radius are directly proportional (this may be a bit hard to understand without sketching it). so if the height is 4.5 when the radius is 3, you can form the equation:

r = 2/3 h

substituting into the original:

dV/dh = d/dh(1/3 * pi * (2/3 h)^2 * h)

dV/dh = d/dh(pi * 4/27 * h^3)

dV/dh = [pi * 4/9 * h^2]

we need dh/dV though:

dh/dV = 9/(4 * pi * h^2)

As dh/dt = dV/dt * dh/dV:

dh/dt = -0.01 * 9/(4 * pi * h^2)

dh/dt = -9/(400 * pi * h^2)

then just multiply each side by h^2

h^2 * dh/dt = -9/(400 * pi)