Question

A soda glass has the shape of the surface generated by revolving the graph of y=6 x^2 for 0< x< 1 about the y-axis. Soda is extracted from the glass through a straw at the rate of 1/2 cubic inch per second. How fast is the soda level in the glass dropping when the level is 2 inches?

Answer 1

it looks like the area that will be revolving is between\[x=\sqrt{\frac y6}\]and the y axis. The radius of each disk will then be that formula, and we get a volume of\[V=\pi\int_{0}^{6}r^2dy=\frac\pi6\int_{0}^{6}ydy\]hm... what next...