ECZ 2018 · O-Level Paper 2 · Question 12 — Mensuration
Question from ECZ 2018 · O-Level Paper 2 · Question 12
(a) The diagram below 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. Given that the height of the frustum is 11.4 cm, calculate its volume.[6]
Verified working — step 1
Prismoidal formula for a frustum with rectangular ends: V = (h6)[(2a + c)b + (2c + a)d], with a = 14, b = 10, c = 8, d = 4, h = 11.4.(b) The points A(15° N, 40° E), B(35° S, 70° E) and C(35° S, 40° E) are on the surface of the earth. [Use π = 3.142 and R = 6370 km]
(b(i)) Calculate the distance AC in kilometres.[2]
Verified working — step 1
A and C share longitude 40 E, so AC runs along a meridian (great circle).(b(ii)) 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.
(b(ii)(a)) Calculate the difference in longitudes between B and Q.[3]
Verified working — step 1
B and Q share latitude 35 S, so the 900 km runs along that parallel.(b(ii)(b)) Find the position of Q.[1]
Verified working — step 1
Flying due west keeps the latitude at 35 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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