Close. Surface area of the complete sphere (hemisphere on both ends) and lateral surface area of the cyllinder.Originally Posted bymonkeybone114

Not very close. Try Volume of the sphere and volume of the cyllinder.Originally Posted bymonkeybone114

The calculus will do you no good if the geometry is off.

What has gone wrong should send up red flags. Obviously r = 0 will minimize the materials, but the constraint has not been applied.

Unless I have forgotten what we are doing here, you must also remember the the method of Lagrange Multipliers gives critical points. It is the student's responsibility to determine min or max.