NECO Mathematics 2007 Theory — Question 3
Question 3 of 50 from the National Examinations Council (NECO) Mathematics 2007 Theory paper, with the correct answer and a full explanation.
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3. (a) The volume of a cone is 565.7cm^3. If the cone is 15cm high, find its base radius correct to the nearest whole number (pi=22/7). (b) The 1st, 2nd and last terms of an A.P. are 1, 4/3 and 3 2/3 respectively. Find the number of terms in the A.P. (8 marks)
Model answer
(a) V=1/3 pi r^2 h: 565.7 = 1/3 x 22/7 x r^2 x 15. Solving: r^2 = (565.7x3x7)/(22x15) ~= 35.999, so r ~= 6cm (to the nearest whole number). (b) a=1, common difference d = 4/3-1 = 1/3. Last term T_n = 11/3. Using T_n=a+(n-1)d: 11/3 = 1+(n-1)(1/3), (n-1)/3 = 8/3, n-1=8, n=9 terms.
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