A cuboid is given with side lengths of $x$ cm, $(5-x)$ cm and $15$ cm.
The diagram depicts a pyramid whose square base has side length $9$ cm. The pyramid has height $x$ cm and volume $y$ cm$^3$.
(a)[1]
Show that the cuboid volume equation, $y$ cm$^3$, is $y = 75x - 15x^2$.
(b)[1]
Complete the value table for $y = 75x - 15x^2$.
(c)[3]
Draw the graph of $y = 75x - 15x^2$ for $1 \le x \le 4$.
(d(i))[1]
Show that the pyramid volume equation is $y = 27x$.
(d(ii))[3]
By drawing a suitable straight line on the grid on page 2, find the height of the pyramid when the pyramid and the cuboid have the same volume.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Thus, $y = x(5-x)\times15 = 75x^2-15x$.” …