2026 NYGH P2 Q6

A cylindrical jar with a radius of \(3\text{ cm}\) contains water to a depth of \(5\text{ cm}\). The water is then poured at a constant rate into an empty right conical container, as shown in the diagram below. After \(t\) seconds, the depth of water in the conical container is \(x\text{ cm}\) and the volume, \(V\text{ cm}^3\), of water in the conical container is given by \(V=\dfrac13\pi x^3\).

Given that all the water in the cylindrical jar is transferred in 3 seconds, find

1. \(\dfrac{\mathrm{d}V}{\mathrm{d}t}\) in terms of \(\pi\),[2]
2. the rate at which \(x\) is increasing at the instant when \(x=2.5\).[3]