2025 AHS PRELIMS P2 Q15

The diagram shows a container with diameter 20 cm and height 40 cm. It contains water to a height of 24 cm from the vertex of the container. A layer of oil of height 4 cm floats on the water surface.

1. Calculate the diameter of the water in the container.[1]
2. The curved surface area of the container is \(150\text{ cm}^2\). Calculate the curved surface of the container in contact with the oil.[3]

Source check: the stated radius \(10\) cm and height \(40\) cm give a full curved surface area of \(\pi(10)\sqrt{10^2+40^2}=100\pi\sqrt{17}\approx1295.31\text{ cm}^2\), not \(150\text{ cm}^2\). Part (b) therefore has incompatible givens. The printed-area calculation gives \(19.5\text{ cm}^2\) conditionally; using the stated dimensions gives \(13\pi\sqrt{17}\approx168.39\text{ cm}^2\).