ECZ 2019 · GCE Paper 2 · Question 10 — Earth Geometry

A frustum TQRS of a cone [π = 3.142]: US = 3cm (top radius), UV = 10cm (height), RV = 8cm (bottom radius). Earth points [π = 3.142, R = 6370 km]: K(50°N, 30°W), L(50°N, 60°E), M(45°S, 60°E).

(a) Given that US = 3cm, UV = 10cm and RV = 8cm, calculate the volume of the frustum.[6]

Verified working — step 1

Let the full cone (before cutting) have height H to the base of radius 8 cm, and let the small cone cut off have height h to the top of radius 3 cm.

(b(i)) Find the difference in longitude between points K and L.[2]

Verified working — step 1

K is at 30°W and L is at 60°E.

(b(ii)(a)) Find, in kilometres, the distance LM.[2]

Verified working — step 1

L(50°N,60°E) and M(45°S,60°E) lie on the same meridian (60°E), so the distance between them is measured along a great circle (meridian).

(b(ii)(b)) Find, in kilometres, the distance KL.[2]

Verified working — step 1

K and L are both on latitude 50°N, with a longitude difference of 90° (from part (i)).

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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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