ECZ 2022 · GCE Paper 2 · Question 9 — Earth Geometry

M, L and K are points on the surface of the earth [π = 3.142 and R = 3437 nm]: M and K on latitude 80°N, M at longitude 48°W, K at longitude 32°E; L at latitude 85°S on longitude 32°E. A frustum of a cone has top and bottom diameters 6cm and 18cm respectively and perpendicular height 10cm [π = 3.142].

(a(i)) Determine the difference in longitudes between points M and K.[2]

Verified working — step 1

Longitude of M = 48°W, longitude of K = …

(a(ii)(a)) Calculate, in nautical miles, the distance between M and K along latitude 80°N.[2]

Verified working — step 1

Distance along a latitude = (difference in longitude in minutes) × cos(latitude)

(a(ii)(b)) Calculate, in nautical miles, the distance between K and L along longitude 32°E.[2]

Verified working — step 1

K and L lie on the same longitude (32°E), so the distance between them is measured along a great circle (meridian).

(b) Given that its perpendicular height is 10cm, calculate the volume of the frustum.[6]

Verified working — step 1

For a frustum with radii R = 9 cm (bottom), r = 3 cm (top), and height h = 10 cm:

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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