A right circular conical vessel is being filled with green industrial waste at a rate of 100 cubic meters per second. How fast is the level rising after 200pi cubic meters have been poured in? The cone has a height of 50m and a radius 30m at its brim. (The volume of a cone of heigh h and cross-sectional radius r at its brim given by V=1/3pir^2h)

Question

Mathematics

Duncan Macdonald

31 March, 06:57

A right circular conical vessel is being filled with green industrial waste at a rate of 100 cubic meters per second. How fast is the level rising after 200pi cubic meters have been poured in? The cone has a height of 50m and a radius 30m at its brim. (The volume of a cone of heigh h and cross-sectional radius r at its brim given by V=1/3pir^2h)

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Answers (1)

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Winston · Answer 1

This is the concept of calculus:

dV/dt*dh/dV=dh/dt

Volume of the cone is given by:

V = (1/3) πr^2h=1/3*π*3^2*h=3π

dV/dh=3*π=3π

dh/dV=1 / (3π)

dV/dt=100 m^2/sec

thus;

dh/dt=1 / (3π) * 100

=33 1/3 m/s