Whats the height of a cone that has a diameter of 40 cm and a volume of 23,000 mm?

In your question you refer to $$23000^2$$ and in the title you refer to 23000 mm.

 

Anyway, 23000 mm = 2300cm and the formula for the volume of a cone is given by

 

$$V = \pi r^2 \frac{h}{3}$$

Depending on your question, either

 

$$2300 = \pi (\frac{40}{2})^2 \frac{h}{3}$$

or

$$2300^2 = \pi (\frac{40}{2})^2 \frac{h}{3}$$

which can be rewritten to

 

either

 

$$h = \frac{3*2300}{\pi (\frac{40}{2})^2}$$

or

$$h = \frac{3*2300^2}{\pi (\frac{40}{2})^2}$$

depending on you original question.

 

I think you can do the calculation yourself...

 

Reinout