ECZ 2023 · GCE Paper 2 · Question 8 — Earth Geometry
A frustum of a cone has perpendicular height 40cm and top and bottom radii 10cm and 30cm respectively [π = 3.142]. Four towns A(70°N, 65°W), B(70°N, 65°E), C(70°S, 65°E) and D(70°S, 65°W) are on the surface of the earth [π = 3.142, R = 3437 nm].
(a) Calculate the volume of the frustum.[6]
Verified working — step 1
Use the frustum volume formula:(b(i)) Sketch the surface of the earth showing all the four towns A, B, C and D.[2]
Verified working — step 1
Draw a circle to represent the earth. Mark the North and South poles (N at top, S at bottom) and draw the equator as a horizontal diameter. Draw the Greenwich meridian (0°) as a vertical line through the centre.(b(ii)(a)) Calculate, in nautical miles, the distance AB along latitude 70°N.[2]
Verified working — step 1
A and B are on the same latitude (70°N), so use the small-circle (latitude) distance formula:(b(ii)(b)) Calculate, in nautical miles, the distance BC along longitude 65°E.[2]
Verified working — step 1
B and C lie on the same meridian (65°E), so the distance is along a great circle (longitude line):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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