ECZ 2024 · O-Level Paper 2 · Question 7 — Mensuration

Question from ECZ 2024 · O-Level Paper 2 · Question 7

(a) The diagram is a rectangular based right pyramid. Given that PQ = 8 cm, QR = 6 cm and SV = PV = QV = RV = 13 cm, calculate the

(a(i)) perpendicular height, MV, of the pyramid,[3]

Verified working — step 1

The height MV stands on the base's centre M, so start from the base diagonal:

(a(ii)) volume of the pyramid.[3]

Verified working — step 1

Pyramid volume = (13) x base area x perpendicular height

(b) The diagram shows the points R, Q, P and T on the surface of the earth. [Take π = 3.142 and R = 3 437 nm]

(b(i)) Find the difference in longitudes between points Q and T.[2]

Verified working — step 1

Q is on longitude 70 W and T on longitude 42 …

(b(ii)) Calculate, in nautical miles, the distance between

(b(ii)(a)) R and P along latitude 85° N,[2]

Verified working — step 1

Along a latitude circle, distance in nautical miles = (longitude difference) x 60 x cos(latitude).

(b(ii)(b)) P and T along longitude 42° E.[2]

Verified working — step 1

P (85 N) and T (20 N) share a meridian, on the SAME side of the equator.

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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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