Diameter of the base of a water - filled inverted right circular cone is 26 cm. A cylindrical pipe, 5 mm in radius, is attached to the surface of the cone at a point. The perpendicular distance
between the point and the base (the top) is 15 cm. The distance from the edge of the base to the
point is 17 cm, along the surface. If water flows at the rate of 10 meters per minute through the
pipe, how much time would elapse before water stops coming out of the pipe?

Radius of cone = $$BP = 13$$ cm

In $$\triangle$$ ABC

=> $$(AB)^2 = (BC)^2 - (AC)^2$$

=> $$(AB)^2 = 17^2 - 15^2 = 289 - 225$$

=> $$AB = \sqrt{64} = 8$$ cm

=> AP = OC = $$BP - AB = 13 - 8 = 5$$ cm

Let time elapsed before water stops coming out of the pipe = $$T$$ min

Volume of frustum = Volume discharged

=> $$\frac{1}{3} \pi h (R^2 + r^2 + R r) = \pi  (0.5)^2 \times f \times T$$    (where f is the flowrate given by 10m/s = 1000cm/s)

(Total volume = Cross sectional area of pipe $$\times$$ flowrate $$\times$$ Total time)

=> $$\frac{1}{3} \times 15 \times (13^2 + 5^2 + 13 * 5) = 0.25 \times 1000 \times T$$

=> $$5 \times 259 = 250 \times T$$

=> $$T = \frac{259}{50} = 5.18$$ mi