Date | November 2016 | Marks available | 3 | Reference code | 16N.2.SL.TZ0.S_6 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Question number | S_6 | Adapted from | N/A |
Question
All lengths in this question are in metres.
Let , for . Mark uses as a model to create a barrel. The region enclosed by the graph of , the -axis, the line and the line is rotated 360° about the -axis. This is shown in the following diagram.
Use the model to find the volume of the barrel.
The empty barrel is being filled with water. The volume of water in the barrel after minutes is given by . How long will it take for the barrel to be half-full?
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
attempt to substitute correct limits or the function into the formula involving
eg
0.601091
volume A2 N3
[3 marks]
attempt to equate half their volume to (M1)
eg, graph
4.71104
4.71 (minutes) A2 N3
[3 marks]