9709 P15 - Nov 2025 - Q7 - 8 marks
9686
An open cylindrical tank has a base but no top, radius \(r\text{ cm}\), height \(h\text{ cm}\), and fixed outside surface area \(600\pi\text{ cm}^2\).
(a) Show its volume is \(V=\frac{\pi r(600-r^2)}2\). [3]
(b) Find the exact \(r\) giving maximum volume. [3]
(c) Hence find the maximum volume. [2]
