Date | May 2019 | Marks available | 2 | Reference code | 19M.1.SL.TZ1.T_15 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Find | Question number | T_15 | Adapted from | N/A |
Question
A cylinder with radius r and height h is shown in the following diagram.
The sum of r and h for this cylinder is 12 cm.
Write down an equation for the area, A, of the curved surface in terms of r.
Find dAdr.
Find the value of r when the area of the curved surface is maximized.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A=2πr(12−r) OR A=24πr−2πr2 (A1)(M1) (C2)
Note: Award (A1) for r+h=12 or h=12−r seen. Award (M1) for correctly substituting into curved surface area of a cylinder. Accept A=2πr(12−r) OR A=24πr−2πr2.
[2 marks]
24π−4πr (A1)(ft)(A1)(ft) (C2)
Note: Award (A1)(ft) for 24π and (A1)(ft) for −4πr . Follow through from part (a). Award at most (A1)(ft)(A0) if additional terms are seen.
[2 marks]
24π−4πr=0 (M1)
Note: Award (M1) for setting their part (b) equal to zero.
6 (cm) (A1)(ft) (C2)
Note: Follow through from part (b).
[2 marks]