2025 MGS(S) PRELIMS P2 Q7

A cylindrical solid has a hemispherical top of the same radius \(r\text{ cm}\). The cylinder has height \(2r\text{ cm}\), and the volume of the entire solid is \(576\pi\text{ cm}^3\).

1. Show that \(r=6\).[3]
2. The entire solid is melted to form a solid cone whose radius and height are equal. Find the total surface area of the cone.[4]