Moderate -0.5 This is a standard C1 optimization setup question requiring substitution of the volume constraint into the surface area formula. It involves routine algebraic manipulation with no actual optimization or problem-solving—students simply need to recall formulas for cylinder volume and surface area, then substitute and simplify. The 'show that' format makes it easier than if they had to derive the expression independently.
A container made from thin metal is in the shape of a right circular cylinder with height \(h\) cm and base radius \(r\) cm. The container has no lid. When full of water, the container holds 500 cm³ of water.
Show that the exterior surface area, \(A\) cm², of the container is given by
$$A = \pi r^2 + \frac{1000}{r}.$$
[4]
A container made from thin metal is in the shape of a right circular cylinder with height $h$ cm and base radius $r$ cm. The container has no lid. When full of water, the container holds 500 cm³ of water.
Show that the exterior surface area, $A$ cm², of the container is given by
$$A = \pi r^2 + \frac{1000}{r}.$$
[4]
\hfill \mbox{\textit{Edexcel C1 Q6 [4]}}