ECZ 2016 · O-Level Paper 2 · Question 9 — Earth Geometry
The points A, B, C and D are on the surface of the earth. (Take pi = 3.142 and R = 3437 nm.)
(a(i)) The diagram shows points A, B, C and D on the surface of the earth. Find the difference in latitude between points C and B.[1]
Verified working — step 1
B is on latitude 50 degrees N an…(a(ii)) Calculate the length of the circle of latitude 50 degrees N in nautical miles.[2]
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The radius of the circle of latitude is r = R cos 50 degrees.(a(iii)) Find the distance AD in nautical miles.[3]
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A and D lie on the same longitude 75 degrees W, so AD runs along a great circle.(b) The cross section of a rectangular tank measures 1.2 m by 0.9 m. If it contains fuel to a depth of 10 m, find the number of litres of fuel in the tank. (1 m3 = 1000 litres.)[3]
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Volume = 1.2 x 0.9 x 10 = …(c) A cone has a perpendicular height of 12 cm and a slant height of 13 cm. Calculate its total surface area. (Take pi = 3.142.)[3]
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By Pythagoras, r2 + 122 = 132, so r2 = 25 and r = 5 cm.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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