2025 CGS PRELIMS P2 Q7

The figure shows a solid consisting of a right circular cone and a hemisphere. The height and the base radius of the circular cone are \(h\text{ cm}\) and \((h+6)\text{ cm}\) respectively. The volume of the hemisphere is three times the volume of the cone.

1. Show that \(h=12\).[3]
2. Find the total surface area of the solid, giving your answer correct to the nearest \(\text{cm}^2\).[3]
3. Cathy buys a tin of paint that can cover a surface area of \(0.5\text{ m}^2\). She cuts the solid into 2 identical parts and plans to paint all surfaces of the two parts with the can of paint. Does she have enough paint? Explain your answer.[3]