2025 MSHS PRELIMS P1 Q23

A hollow container is made by joining a hemisphere of radius \(r\text{ cm}\) to an open cylinder of radius \(r\text{ cm}\) and height \(h\text{ cm}\).

1. If the ratio of the capacity of the hemisphere to the capacity of the cylinder is \(1:4\), show that \(h=\dfrac83r\).[2]
2. If the total capacity of the container is \(\dfrac{80\pi}{3}\text{ cm}^3\), find the radius.[2]
3. Find the area of the metal sheet used to make the container. Leave your answer in terms of \(\pi\).[2]