The cuboid’s dimensions are $x$ cm, $2x$ cm and $4x$ cm, as the diagram indicates.
(i)[3]
Show that the surface area $S\ \text{cm}^2$ and the volume $V\ \text{cm}^3$ satisfy the relation $S = 7V^{\frac{2}{3}}$.
(ii)[4]
At the instant when the cuboid volume is $1000\ \text{cm}^3$, the surface area is increasing at $2\ \text{cm}^2\,\text{s}^{-1}$. Find the rate at which the volume is increasing at this instant.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct formulae are $S=28\pi x^2$ for surface area and $V=8x^3$ for volume.” …