Price of aluminum alloy splayed shaft sleeve

According to the meaning of the question, let the radius of the bottom surface be r,

Let the cost of iron per unit area be m and the total cost of barrel be y, then y = 3m π R2+m (π R2+2π RH).

Because the container is a cylindrical iron drum with an aluminum alloy cover, the volume is 32π,

Then we know that V=πr2h=32π and the height is 32r2.

Y = 3m π R2+m (π R2+2π RH) = 2m π (R2+16r+16r) ≥ 6m π 3R2×16r.

The minimum value is obtained when and only when r=3 16, so the radius is 3 16 when the total cost is the lowest.