# Sand of Time

Calculus Level 4

An hour glass is constructed from rotating the graphs $$y = \frac{x^{2}}{3}$$ and $$y = -\frac{x^{2}}{3}$$ around the y-axis within the domain of $$[-6, 6]$$ as shown in the picture above.

The upper inverted bulb of the hour glass has a circular base with radius of $$6$$ cm. and is $$12$$ cm. high, and the sand, filled in the upper bulb, is dripping into the lower bulb at a constant rate, falling all down in an hour.

What is the rate of decrease in height of the upper bulb in cm./minute when half an hour has passed?