2025 CCHY PRELIMS P1 Q16

Three spheres, each of radius \(2r\text{ cm}\), are placed inside a cylinder. The cylinder has radius \(3r\text{ cm}\) and height \(12r\text{ cm}\). Water is poured into the cylinder to fill it completely. The volume of water poured into the cylinder is \(k\pi r^3\text{ cm}^3\). Find the value of \(k\).[3]