Question

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=1/3*pi*r^2h)

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