Date | May 2009 | Marks available | 7 | Reference code | 09M.1.sl.TZ1.7 |
Level | SL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 7 | Adapted from | N/A |
Question
The graph of y=√x between x=0 and x=a is rotated 360∘ about the x-axis. The volume of the solid formed is 32π . Find the value of a.
Markscheme
attempt to substitute into formula V=∫πy2dx (M1)
integral expression A1
e.g. π∫a0(√x)2dx , π∫x
correct integration (A1)
e.g. ∫xdx=12x2
correct substitution V=π[12a2] (A1)
equating their expression to 32π M1
e.g. π[12a2]=32π
a2=64
a=8 A2 N2
[7 marks]
Examiners report
Despite the “reverse” nature of this question, many candidates performed well with the integration. Some forgot to square the function, while others did not discard the negative value of a. Some attempted to equate 32π to the formula for volume of a sphere, which suggests this topic was not fully covered in some centres.