O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2014 · Q99 Marks
A solid circular cylinder has a base radius of r cm and a volume of 4000 cm³.
- (i)Show that the total surface area, A cm², of the cylinder is given by A = 8000/r + 2π r².[3]
- (ii)Given that r can vary, find the minimum total surface area of the cylinder, justifying that this area is a minimum.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B1] (i) B1 for h = 4000/(π r²) or π r² h = 4000
- [M1] (i) M1 for substitution of h or π rh into their equation for A
- [A1] (i) A1 Answer given
- [B1, B1] (ii) B1 for each term correct
- [M1] (ii) M1 for equating to zero and attempt to find r³
- [M1] (ii) M1 for substitution of their r to obtain A.
- [A1] (ii) A1 for 1390 or awrt 1395
- [\u221aB1] (ii) \u221aB1 for a complete correct method and conclusion.
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