Question: A cone-shaped hour-glass of radius \(6 \mathrm{~cm}\) and depth \(10 \mathrm{~cm}\) contains sand which runs out through a hole at the bottom at a constant rate of \(1.5 \mathrm{~cm}^{3}\) per second. Answer the questions below with an accuracy of two decimal places. Show all work and remember to include units in your answers. Hint: The volume of a cone is given by \(V=\frac{1}{3} \pi r^{2} h\) where \(r\) is the radius and \(h\) the height.

1. If the hour-glass starts out full, how long does it take to empty?
2. Find the volume of sand in the hour-glass when the depth of sand is \(h \mathrm{~cm}\).
3. How fast is the sand level falling when the depth is \(8 \mathrm{~cm}\) ?

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