minutes to fill a fountain

solid-geometry

Solution 1:

Note that part of the second cylinder includes the middle cylinder so by the time that the middle cylinder is filled, you have already filled a portion of the second cylinder. The total volume of the fountain is $(\pi(r\sqrt{2})^2h_2)+(\pi r^2(3h_2))-(\pi r^2 h_2)=4\pi r^2h_2$

Hence, we have $\frac{3\pi r^2h_2}{4\pi r^2h_2}=\frac{30}{x}\implies x=40$

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