An antique anchor is to be preserved in a plastic mold. The mold is 3 m high and is to be placed on top of a stand of height 1 m. Inside the mold, the anchor is to be placed on top of a marble box. The figure below shows the longitudinal cross-section of this arrangement. The parabolic arcs of the mold are given by the equation $\displaystyle y = \frac{4}{7x^2} - \frac{3}{7}$.

(Apologies for the crude drawing and wording -- I left my book at school so I'm doing this from memory.)

From previous questions I have:

- the volume of the mold, and
- the volume of the mold at any height,
h, above the ground.

1)Plastic flows into the mold at 300 litres/min. Find the height of the anchor and hence the height of the marble block if the top of the anchor is covered after exactly 10 minutes.

I was thinking something along the lines of $\displaystyle \frac{dh}{dt} = \frac{dV}{dt}\cdot\frac{dh}{dV}$.

2)If the plastic now flows at 329 litres/min, expresshin terms oft.

If you could point me in the right direction, that would be great. Thanks.