All measurements in this question are in centimetres. The diagram illustrates a cuboid solid with a square base. Its vertical height is marked $9 - x$, and each edge of the base is marked $x$. The diagram is labelled NOT TO SCALE.
(a(i))[1]
Fill in the table.
(a(ii))[4]
On the grid on the opposite page, draw the graph of $V = x^2(9-x)$ for $0 \leq x \leq 9$.
(a(iii))[2]
Find the values of $x$ when the volume of the cuboid is $44\text{ cm}^3$.
(b(i))[2]
Show that the total surface area of the cuboid is $(36x - 2x^2)\text{ cm}^2$.
(b(ii))[3]
Find the surface area when the cuboid volume is at its maximum.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$28$” …