At a sand and gravel plant, sand is falling off the conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately twice the height of the pile. At what rate is the height of the pile changing when it is approximately 20 feet high?
10?ft?^3,dv/dt=10
find dh/dt when h=20
v=(?v^2 h)/3,v=h,v=(?/3) h^3
dv/dt=(?/3)3h^2 dh/dt=?h^2 (dh/dt)
dh/dt=1/(?h^2 ) (dv/dt)
dv/dt=10,h=20
dh/dt=1/(?(20)^2 ) (10)=1/1256.60 (10)=7.196*?10?^(-3)
10?ft?^3,dv/dt=10
find dh/dt when h=20
v=(?v^2 h)/3,v=h,v=(?/3) h^3
dv/dt=(?/3)3h^2 dh/dt=?h^2 (dh/dt)
dh/dt=1/(?h^2 ) (dv/dt)
dv/dt=10,h=20
dh/dt=1/(?(20)^2 ) (10)=1/1256.60 (10)=7.196*?10?^(-3)
