Calculus question regarding volume of cone, please help :)

You decide to warm your house by lighting your wood fireplace. The smoke is coming out of the chimney in the shape of an inverted right circular cone, the diameter of which is equal to its height. If the rate of smoke emission is (100)m^3/min, how fast is the height increasing when the height is 30m? (volume of a cone is V=1/3(pi)(r^2)(h) )

dV/dt = 100

V = (1/3) * pi * r^2 * h

r = d/2
h = d

r = h/2

V = (1/3) * pi * (h/2)^2 * h
V = (1/3) * (1/4) * pi * h^3
V = (1/12) * pi * h^3
dV/dt = 3 * (1/12) * pi * h^2 * dh/dt
dV/dt = (pi/4) * h^2 * dh/dt

h = 30
dV/dt = 100
dh/dt = ?

Now it's just plug and chug

100 = (pi/4) * 30^2 * dh/dt
100 = 900 * pi / 4 * dh/dt
1 = (9pi/4) * dh/dt
dh/dt = 4 / (9 * pi)

Just an idea:

Express the height in terms of its diameter (to reduce the number of variables), and find dh/dt.