Volume of Cylinder V₁ =πR². H
Volume of a cone V₂ = (1/3).πR².h
We know that H=4h (given) & R, the radius =75 &The total Volume = V₁+V₂,
We also know that the hopper has one cylinder & 2 equal cones
Hence
πR². H + 2 [(1/3).πR².h] =343,000 ft³
π(75)².H + 2[(1/3).π(75)².h] =343,000
But H = 4h, then
π(75)².4h + 2[(1/3).π(75)².h] =343,000. Solve for h
26250.π.h = 81,466.8.h = 343,000
& h=343,000/81,466.8, ==> h=4.16 ft & H =16.6 FT
