Paper 2 · Mensuration
(a) The diagram shows a wine glass in the shape of a cone mounted on a stand. The depth of the cone is equal to its diameter at the top. (i) Write down an expression for the volume of the cone in terms of its radius r and pi. (ii) If the wine glass can hold 20 ml of wine when full, calculate the radius of the wine glass at the top. (iii) Wine is bought in bottles of volume 750 ml. Calculate the number of wine glasses that can be filled from one bottle. [Volume of cone = (1/3) base area x height. pi = 22/7] (b) The base of triangle is x cm and its height is (x - 7) cm. (i) Write down an expression for the area of the triangle. (ii) If the area of the triangle is 6 cm^2, form an equation in x and show that it reduces to x^2 - 7x - 12.
Model answer
2 pi r^3 / 3
Also accepted: (2/3) pi r^3, 2pi r^3/3, 2πr^3/3, 2,12 cm, 2.12 cm, 2,12, 2.12, 2,121 cm, 2,1 cm, 37 glasses, 37, 37,5, x(x - 7)/2, (x^2 - 7x)/2, x(x-7)/2, 0,5x(x - 7), x^2 - 7x - 12 = 0, x^2-7x-12, 2 pi r^3 / 3; 2,12 cm; 37; (x^2 - 7x)/2, (2/3)pi r^3; 2,12 cm; 37; (1/2)x(x - 7); x^2 - 7x - 12 = 0
ZIMSEC Mathematics 4008/2, November 2010, Q7, via the Topical Collection