ECZ 2020 · GCE Paper 2 · Question 10 — Earth Geometry

Three points P, Q and R on the surface of the earth [π = 3.142, R = 6370 km]: P on latitude X°N at longitude 55°W, Q on latitude X°N at longitude 24°E, R on latitude 60°S at longitude 24°E. A frustum ABCDEFGH of a pyramid: EFGH and ABCD are squares of sides 8cm and 12cm respectively, height 3cm.

(a(i)) Calculate the difference in longitude between P and R.[2]

Verified working — step 1

P is at longitude 55°W and R is at longitude 24°E.

(a(ii)) Given that the distance between P and Q on latitude X°N is 4392.079611 km, calculate X.[2]

Verified working — step 1

Distance along a latitude = (difference in longitude360) × 2πR cos X

(a(iii)) Calculate the distance QR on longitude 24°E.[2]

Verified working — step 1

Q and R are on the same longitude (24°E), so QR is a distance along a great circle (meridian).

(b) Given that the height of the frustum is 3cm, calculate its volume.[6]

Verified working — step 1

The frustum is formed by cutting a small pyramid (top, base 8 cm) from a large pyramid (base 12 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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