ECZ 2021 · O-Level Paper 2 · Question 7 — Earth Geometry
Question from ECZ 2021 · O-Level Paper 2 · Question 7
(a) The points P, Q, R and T are on the surface of the earth as shown in the diagram below. (Take π = 3.142 and R = 3 437 nm)
(a(i)) Determine the difference in longitudes between points Q and R.[2]
Verified working — step 1
Q (70 N) and R (40 S) both…(a(ii)) Find the length of the circle of latitude 40° S in nautical miles.[2]
Verified working — step 1
The circle of latitude 40 S has radius R cos 40.(a(iii)) Calculate the distance TR in nautical miles.[2]
Verified working — step 1
T (60 W) and R (55 E) sit on latitude 40 S, across Greenwich, so longitudes ADD:(b) The diagram below shows a cone. The shaded part is the thickness of the cone. The internal volume is 34 650 cm3. The internal base area is 3 850 cm2. [Take π = 3.142]
(b(i)) Calculate the internal height (h) and radius (r).[4]
Verified working — step 1
Volume of a cone V = (13)Ah, so 34650 = (13)(3850)h, giving h = 3 × 346503850 = …(b(ii)) Given that the cone is 0.7 cm thick, calculate the external volume of the cone.[2]
Verified working — step 1
Add the 0.7 cm thickness to both radius and height: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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