ECZ 2021 · GCE Paper 2 · Question 12 — Earth Geometry

Points A, B, C and D on the surface of the earth [π = 3.142, R = 6370 km or 3437 nm]: A and B on latitude 52°N, C and D on the equator, with A due north of C and B due north of D; the difference in longitude between the meridian of ACand the meridian of BDis 85° (central angles 85° and 52° shown on the diagram).

(a(i)) Determine the difference in longitude between points A and B.[1]

Verified working — step 1

Since A is due north of C and B is due north of D, A and C lie on the same meridian, and B and D lie on the same meridian.

(a(ii)(a)) Calculate the distance between C and D along the equator in nautical miles.[2]

Verified working — step 1

C and D lie on the equator, so 1 minute of arc = 1 nautical mile.

(a(ii)(b)) Calculate the distance between B and D along their common longitude, in kilometres.[3]

Verified working — step 1

B and D lie on the same meridian, with B at latitude 52°N and D at latitude 0° (equator).

(b) A frustum of a cone has circles of radii 1.5cm (top) and 5cm (bottom) and height 7cm. Calculate the volume of the frustum. [π = 3.142][6]

Verified working — step 1

For a frustum of a cone:

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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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