ECZ 2014 · O-Level Paper 2 · Question 9 — Earth Geometry
Question from ECZ 2014 · O-Level Paper 2 · Question 9
(a) A pattern on a chitenge material consists of three circles as shown in the diagram below. AC is the diameter of the bigger circle. Given that the diameter of each of the small circles is 20 cm and taking π = 3.142, calculate the
(a(i)) total perimeter of the two small circles,[3]
Verified working — step 1
Circumference of one small circle = π d = 3.142 × 20 = 62.84 cm.(a(ii)) area of the shaded part.[3]
Verified working — step 1
AC = 20 + 20 = 40 cm, so the big circle has radius 20 cm.(b) The diagram below shows a model of the earth. The points C and D are on the same longitude. The latitudes of C and D are 45° N and 55° S respectively. (Take π = 3.142 and R = 3 437 nm)
(b(i)) Write the position of the point C.[1]
Verified working — step 1
Read the position as (latitude, longitude).(b(ii)) Calculate the difference in latitude between C and D.[1]
Verified working — step 1
C is at 45 N and D at 55 S, on opposite sides of the equator.(b(iii)) Find the distance CD in nautical miles.[2]
Verified working — step 1
C and D lie on the same meridian, so measure along a great circle.(b(iv)) Calculate the circumference of the latitude 45° N in nautical miles.[2]
Verified working — step 1
The circle of latitude 45 N has radius R cos 45.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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