A solid right circular cylinder has radius r r\,r cm and height h h\,h cm. The total surface area of the cylinder is 800 cm2^22.
Show that the volume, V V\,V cm3^33, of the cylinder is given by
V=400r−πr3V = 400r - \pi r^3V=400r−πr3
Use calculus to find the maximum value of VVV, giving your answer to the nearest cm3^33.
Justify that the value of V V\,V you have found is a maximum.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.