Turn over 27 Question 8 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 8 is 9 marks) 28 9. y x A B C D E O Figure 2 Figure 2 shows the vertical cross‑section, AOBCDE, through the centre of a wax candle. In a model, the candle is formed by rotating the region bounded by the y‑axis, the line OB, the curve BC, and the curve CD through 360° about the y‑axis. The point B has coordinates (3, 0) and the point C has coordinates (5, 15). The units are in centimetres. The curve BC is represented by the equation y = 225 2025 2 x a − 3  x < 5 where a is a constant. (a) Determine the value of a according to this model. (2) The curve CD is represented by the equation y = 16 – 0.04x2 0  x < 5 (b) Using algebraic integration, determine, according to the model, the exact volume of wax that would be required to make the candle. (9) (c) State a limitation of the model. (1) When the candle was manufactured, 700 cm3 of wax were required. (d) Use this information and your answer to part (b) to evaluate the model, explaining your reasoning. (1)