Question: Use the differential equation for a leaking container, Eq. (3). At t = 0, a conical tank of height 300 cm and top radius 100

Use the differential equation for a leaking container, Eq. (3).

dy dt B 2gy A(y)

At t = 0, a conical tank of height 300 cm and top radius 100 cm [Figure 11(A)] is filled with water. Water leaks through a hole in the bottom of area B = 3 cm2. Let y(t) be the water level at time t.

(a) Show that the tank’s cross-sectional area at height y is A(y) = π/9y².
(b) Solve the differential equation satisfied by y(t).
(c) How long does it take for the tank to empty?

300 cm 100 cm Hole (A) Conical tank y Radius 4 m 15 m Hole (B) Horizontal tank

dy dt B 2gy A(y)

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