ECZ 2013 · O-Level Paper 2 · Question 11 — Earth Geometry
Question from ECZ 2013 · O-Level Paper 2 · Question 11
(a) M, R and Z are points on the surface of the earth as shown in the diagram below. M is on the parallel of latitude 55° N, Z and R are on the same parallel of latitude 65° S, M and R are on the same longitude 30° E and Z is on longitude 45° W [π = 3.142, R = 6 370 km].
(a(i)) Find the difference in latitude between points M and R.[1]
Verified working — step 1
M is at 55 N and R at 65 S, on opposite sides of the equator.(a(ii)) Calculate the distance MR along the same longitude, giving your answer to the nearest kilometre.[2]
Verified working — step 1
M and R share a meridian, so measure along a great circle.(a(iii)) If the local time at Z is 08 00 hours, what is the time at R?[1]
Verified working — step 1
Z is at 45 W and R at 30 E, so the longitude difference is 45 + 30 = 75°.(a(iv)) Find the distance ZR in kilometres, along the same latitude, giving your answer to the nearest kilometre.[2]
Verified working — step 1
Z and R share latitude 65 S, so measure along that parallel.(b) The diagram below shows part of a flag of an organisation which is in a form of a sector PQR. The circle centre O inside the sector is of radius 30 cm. Given that PQ = PR = 1.26 m, angle RPQ = 40° and taking π = 3.142, calculate
(b(i)) the perimeter of sector PQR,[3]
Verified working — step 1
Arc length = (40360) x 2 × 3.142 × 1.26 = 0.87976 m.(b(ii)) the area of the shaded part, giving your answer in square centimetres.[3]
Verified working — step 1
Work in centimetres: the sector radius is 126 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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