The radius changing when the pile is 0.031 m^3/min high
What is a conical pile?
Bulk material that has been discharged from the end of a static conveyor falls freely, forming conical stockpiles. The descent of material through the gusty air produces blinding plumes of dust in open-air conical stacks. Geometrical domes assist your plant to achieve its environmental objectives by obstructing the wind and containing this dust.
h=3d/8 = 3r/4
dh/dt = 3/4dr/dt
dV/dt = 11 m^3/min
V=1/3pi*r^2*h
dV/dt = pi/3 [2rhdr/dt + r^2 dh/dt]
In an instant, h is given
h=8m
r=32/3 m
dV/dt = pi/3 [2rhdr/dt + r^2 dh/dt]
11 = pi/3 [2*32/3*8dr/dt + 32*32/9* 3/4 dr/dt]
dr/dt = 0.041 m^3/min
dh/dt = 0.031 m^3/min
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