ECZ 2023 · O-Level Paper 2 · Question 7 — Earth Geometry
Question from ECZ 2023 · O-Level Paper 2 · Question 7
(a) The points A, B, C and D are on the surface of the earth as shown in the diagram. (Take π = 3.142 and R = 6 370 km)
(a(i)) Find the difference in latitude between points A and D.[2]
Verified working — step 1
A is at 50 N and D at 50 S — …(a(ii)) Calculate in kilometres, the distance between
(a(ii)(a)) A and B along latitude 50° N,[2]
Verified working — step 1
A (20 W) and B (40 E) sit on latitude 50 N, across Greenwich, so longitudes ADD:(a(ii)(b)) B and C along longitude 40° E.[2]
Verified working — step 1
B (50 N) and C (50 S) share meridian 40 E, on opposite sides of the equator.(b) The following diagram is a frustum of a rectangular pyramid with a base 15 cm long and 6 cm wide. The top of the frustum is 10 cm long and 4 cm wide. Its perpendicular height is 8 cm.
(b(i)) Find the height of the pyramid.[2]
Verified working — step 1
Top and base are similar, ratio 1015 = 46 = 23, so the cut-off pyramid has height (23)H.(b(ii)) Calculate the volume of the frustum.[4]
Verified working — step 1
Frustum = full pyramid - cut-off pyramid, with V = (13) x base area x height.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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