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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2019 · Q98 Marks

In this question all lengths are in centimetres. A closed cylinder has base radius r, height h and volume V. It is given that the total surface area of the cylinder is 600π and that V, r and h can vary.

  1. (i)Show that V = 300πr-πr³.[3]
  2. (ii)Find the stationary value of V and determine its nature.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] 600π = 2πr² + 2πrh
  2. [M1] making h subject from a two term expression for SA.
  3. [A1] correct substitution and manipulation to obtain given answer
  4. [M1] differentiation of given formula to A+Br²
  5. [M1] equating to zero and attempt to solve
  6. [A1] r = 10
  7. [A1] V = 2000π or 6280 or 6283
  8. [B1] cao for d²V/dr² = -6πr, d²V/dr² = −60π or other correct method leading to maximum

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2019 Paper 1 Variant 1, question 9.

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