Standard +0.3 This is a straightforward optimization setup question requiring substitution of a constraint (volume = 500) into the surface area formula. It involves basic formulas for cylinder volume and surface area, simple algebraic manipulation, and no actual optimization or calculus. Slightly easier than average as it's purely algebraic setup work with standard geometric formulas.
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 Q32 [4]}}