Question

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?

Accepted Answer

D. Base radius $R = 13$ cm. In upper right triangle, slant length $= 17$, vertical height $= 15 \implies$ radius at pipe height $= 13 - \sqrt{17^2 - 15^2} = 13 - 8 = 5$ cm. Frustum height $h = 15$ cm. Volume of water above pipe $= \frac{1}{3} \pi h (R^2 + r^2 + Rr) = \frac{1}{3} \pi (15) (13^2 + 5^2 + 13 	imes 5) = 5 \pi (169 + 25 + 65) = 1295 \pi 	ext{ cm}^3$. Flow rate $= \pi r_{pipe}^2 	imes v = \pi (0.5)^2 	imes 1000 = 250 \pi 	ext{ cm}^3/	ext{min}$. Time $= \frac{1295 \pi}{250 \pi} = 5.18$ minutes.

Inverted Cone Water Flow Time

Explanation

Practise this under exam conditions