ECZ 2018 · O-Level Paper 2 · Question 12 — Mensuration
The diagram is a frustum of a rectangular pyramid with a base 14 cm long and 10 cm wide. The top of the frustum is 8 cm long and 4 cm wide.
(a) The diagram is a frustum of a rectangular pyramid with a base 14 cm long and 10 cm wide, and a top 8 cm long and 4 cm wide. Given that the height of the frustum is 11.4 cm, calculate its volume.[6]
Verified working — step 1
Using the prismoidal formula for a frustum with rectangular ends:(b(i)) The points A(15 degrees N, 40 degrees E), B(35 degrees S, 70 degrees E) and C(35 degrees S, 40 degrees E) are on the surface of the earth. (Use pi = 3.142 and R = 6370 km.) Calculate the distance AC in kilometres.[2]
Verified working — step 1
A and C share the longitude 40 degrees E, so AC runs along a great circle.(b(ii)(a)) An aeroplane takes off from point B and flies due west on the same latitude covering a distance of 900 km to a point Q. Calculate the difference in longitudes between B and Q.[3]
Verified working — step 1
Along the circle of latitude 35 degrees S:(b(ii)(b)) Find the position of Q.[1]
Verified working — step 1
Flying due west keeps the latitude at 35 degrees S.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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