Question 1123579
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As the water flows into the conical cup, the surface of the water remains flat.<br>
That means the cones of water at different times are all similar.<br>
Since the radius of the whole cup is half the height of the whole cup, the radius of the surface of the water at any time is half the depth of the water at that time.  So at all times r = (h/2).<br>
The formula for the volume of a cone is<br>
{{{V = (1/3)(pi)(r^2)(h)}}}<br>
Substitute r = h/2 in that formula to get a function for the volume of water as a function of the depth of the water.