ECZ 2023 · O-Level Paper 2 · Question 7 — Earth Geometry
The points A, B, C and D are on the surface of the earth as shown in the diagram. (Take pi = 3.142 and R = 6 370 km.)
(a(i)) The points A, B, C and D are on the surface of the earth as shown in the diagram. Find the difference in latitude between points A and D.[2]
Verified working — step 1
A lies on latitude 50 degrees N…(a(ii)(a)) Calculate in kilometres the distance between A and B along latitude 50 degrees N.[2]
Verified working — step 1
A is at 20 degrees W and B at 40 degrees E, so the difference in longitude is 20 + 40 = 60 degrees.(a(ii)(b)) Calculate in kilometres the distance between B and C along longitude 40 degrees E.[2]
Verified working — step 1
B is at 50 degrees N and C at 50 degrees S on the same …(b(i)) The diagram is a frustum of a rectangular pyramid with a base 15 cm long and 6 cm wide. The top is 10 cm long and 4 cm wide, and its perpendicular height is 8 cm. Find the height of the pyramid.[2]
Verified working — step 1
The top and base are similar rectangles: 1015= 46= 23.(b(ii)) Calculate the volume of the frustum.[4]
Verified working — step 1
Full pyramid: V = (13)(15 x 6)(24) = (13)(90)(24) = 720 cm3The 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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