SOLUTION: A block of metal is cast into a solid cylinder whose volume is 10cm^3. Show that the cylinder has a minimum surface area when r= 3 root (5 over pi). The ends are included.

Question 1137934: A block of metal is cast into a solid cylinder whose volume is 10cm^3. Show that the cylinder has a minimum surface area when r= 3 root (5 over pi). The ends are included.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1)

(2)

Solve equation (1) for h in terms of r and substitute into equation (2), giving you an expression in terms of r only for the surface area.

Set the derivative equal to 0 and solve.

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