Date | May Specimen paper | Marks available | 1 | Reference code | SPM.1.AHL.TZ0.14 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Write down | Question number | 14 | Adapted from | N/A |
Question
The graph of y=−x3 is transformed onto the graph of y=33−0.08x3 by a translation of a units vertically and a stretch parallel to the x-axis of scale factor b.
Write down the value of a.
Find the value of b.
The outer dome of a large cathedral has the shape of a hemisphere of diameter 32 m, supported by vertical walls of height 17 m. It is also supported by an inner dome which can be modelled by rotating the curve y=33−0.08x3 through 360° about the y-axis between y = 0 and y = 33, as indicated in the diagram.
Find the volume of the space between the two domes.
Markscheme
a = 33 A1
[1 mark]
13√0.08=2.32 M1A1
[2 marks]
volume within outer dome
23π+163+π×162×17=22250.85 M1A1
volume within inner dome
π∫330(33−y0.08)23dy=3446.92 M1A1
volume between = 22 250.85 − 3446.92 = 18 803.93 m3 A1
[5 marks]