ECZ 2016 · GCE Paper 2 · Question 12 — Earth Geometry
Metal disc radius 14mm with a square hole side 4mm [π = 3.142]; earth-geometry points A(65°N,5°E), B(65°N,45°W), C due south of A with AOC = 82° [R = 3437 nm].
(a(i)) Calculate the shaded area in mm2.[3]
Verified working — step 1
Area of circle = πr² = 3.142 × 14² = 615.832 mm²(a(ii)) Given thickness 5mm, calculate in mm3 the material required to make 20 such discs.[3]
Verified working — step 1
Volume of one disc = shaded area × thickness = 599.832 × 5 = …(b(i)) State the longitude of A.[1]
Verified working — step 1
From the diagram, A lies o…(b(ii)) Calculate the latitude of C.[1]
Verified working — step 1
C is due south of A on the same meridian, so angle AOC (82°) = …(b(iii)(a)) Calculate, in nautical miles, the shortest distance between A and C along the common longitude.[2]
Verified working — step 1
A and C are on the same meridian, so distance = angle × 60 nm (1° = …(b(iii)(b)) Calculate, in nautical miles, the distance between A and B along the circle of latitude.[2]
Verified working — step 1
A and B are both on latitude 65°N. Longitude difference = 5°E to 45°W = …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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