They gave us the necessary formulas . . .A grain silo has the shape of a right circular cylinder surmounted by a hemisphere.
If the silo is to have a capacity of ft³, find the radius and height of the silo
that requires the least amount of material to construct.
Hint: The volume of the silo is: . .
. . . and the surface area (including the floor) is: . .
From , we have: . .
Substitute into : .
. . which simplifies to: .
Differentiate and equate to zero: .
Then we have: .
From ., we have: .
. . and after a LOT of algebra, we get: .
Fascinating . . . the height is exactly five times the radius.