0580 P43 - Nov 2013 - Q3 - 13 marks
15961
A metal sheet measures 9 cm by 7 cm. A square of side x cm is cut from each corner, then the sheet is folded into an open box of height x cm.
(a) Give the length and width of the box in terms of x. [2]
(b) Show \(V=4x^3-32x^2+63x\). [2]
| x | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 |
|---|---|---|---|---|---|---|---|---|
| V | 0 | … | 35 | 36 | 30 | … | 9 | 0 |
(c) Complete the table. [2]
(d) Draw the graph for \(0\le x\le3.5\). Three points are already plotted. [3]
(e) Volume is at least 30 cm³. Give the possible x values as an inequality. [2]
(f(i)) Read the maximum volume. [1]
(f(ii)) Read the x giving that volume. [1]
