A spherical tank of radius R is half-filled with water. Suppose that water leaks through a hole in the bottom of area B. Let y(t) be the water level at time t (seconds).

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dy √2gB √y (a) Show that dt л(2Ry - y²) (b) Show that for some constant C, = 2π (10Ry3/2-3y5/2) = C-t 15B √2g (c) Use the initial condition y(0) = R to compute C, and show that C = te, the time at which the tank is empty. (d) Show that te is proportional to R5/2 and inversely proportional to B.