A tank, shaped like a cone has height 11 meter and base radius 4 meter. It is placed so that the circular part is upward. It is full of water, and we have to pump it all out by a pipe that is always leveled at the surface of the water. Assume that a cubic meter of water weighs 10 000 N

Question

Terrance Patrick

Mathematics

17 February, 10:44

A tank, shaped like a cone has height 11 meter and base radius 4 meter. It is placed so that the circular part is upward. It is full of water, and we have to pump it all out by a pipe that is always leveled at the surface of the water. Assume that a cubic meter of water weighs 10 000 N

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Antony Casey · Answer 1

The tank is a cone, so the radius of the cross section increases linearly with h

At y=0, r=4 and at y=11, r=0

So

r (y) = 4/11 (11-y)

A (y) = π[4 (11-y) 11]^2

Integral will be:

11∫0 (1000) (9.8) (4πy^2) (25) (11-y) dy