2025 IGCSE Additional Mathematics October/November 0606/21 Q11

A cylinder has radius \(r\text{ cm}\) and height \(h\text{ cm}\).

The total surface area, including the two ends, is \(A\text{ cm}^2\).

The volume of the cylinder is \(330\text{ cm}^3\).

1. Show that \(A=2\pi r^2+\dfrac{660}r\).[3]
2. Given that \(r\) can vary, find the value of \(r\) that gives a stationary value for \(A\) and show that this value is a minimum.[5]