Capacity and material of a composite container

An open-top container consists of a cylinder of internal radius 6 cm and height 8 cm above a conical frustum. The frustum has top radius 6 cm, bottom radius 2 cm and perpendicular height 3 cm. Its bottom is closed by a circular disk. The two parts meet at an unobstructed circular opening. Wall thickness is negligible; ignore joining seams.

The frustum is obtained by removing a small cone from a larger similar cone. You may use frustum curved area \(=\pi(R+r)s\), where \(s\) is its slant height. Also, \(1000\text{ cm}^3=1\) litre.

1. A supplier claims that the container holds at least 1 litre and uses no more than 450 cm² of sheet material. Determine whether both parts of the claim are correct. Support your decision with a complete mathematical model and numerical evidence.[8]
2. A pupil treats the whole container as a cylinder of radius 6 cm and height 11 cm. Explain why this overestimates the capacity and why counting an extra disk at the join is also wrong.[2]