ECZ 2022 · O-Level Paper 2 · Question 11 — Earth Geometry
Question from ECZ 2022 · O-Level Paper 2 · Question 11
(a) The diagram shows the points P(20° N, 80° E), Q(40° S, 80° E) and R(40° S, 30° E) on the surface of the earth. [Take π as 3.142 and R = 6370 km]
(a(i)) Find the difference in longitudes between points R and Q.[2]
Verified working — step 1
R (30 E) and Q (80 E) are both ea…(a(ii)) Calculate the distance PQ in kilometres.[2]
Verified working — step 1
P (20 N) and Q (40 S) share meridian 80 E, on opposite sides of the equator.(a(iii)) Find the length of the circle of latitude 40° S in kilometres.[2]
Verified working — step 1
The circle of latitude 40 S has radius R cos 40.(b) The diagram shows a bin BCDE which was made by cutting off the smaller cone ADE from the cone ABC. [Take π = 3.142] Given that AF = 9 cm, BG = 8 cm, EF = 3 cm and GF = h cm, calculate the
(b(i)) value of h,[2]
Verified working — step 1
Cones ADE and ABC are similar, so their heights scale with their radii.(b(ii)) volume of the bin BCDE.[4]
Verified working — step 1
Bin = big cone ABC - small cone ADE, with V = (13) π r2 h.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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