ECZ 2023 · GCE Paper 2 · Question 8 — Earth Geometry
Question from ECZ 2023 · GCE Paper 2 · Question 8
(a) The diagram shows the frustum of a cone. The perpendicular height is 40 cm. The top and bottom radii are 10 cm and 30 cm respectively. [Take π as 3.142] Calculate the volume of the frustum.[6]
Verified working — step 1
Frustum of a cone: V = (13) π h (R2 + Rr + r2).(b) Four towns A(70° N, 65° W), B(70° N, 65° E), C(70° S, 65° E) and D(70° S, 65° W) are on the surface of the earth. Take π as 3.142 and R = 3 437 nm.
(b(i)) Sketch the surface of the earth showing all the four towns A, B, C and D.[2]
Verified working — step 1
Sketch the sphere with the poles, equator and Greenwich meridian.(b(ii)) Calculate, in nautical miles, the distance
(b(ii)(a)) AB along latitude 70° N,[2]
Verified working — step 1
A and B share latitude 70 N, from 65 W to 65 E across Greenwich, so longitudes ADD:(b(ii)(b)) BC along longitude 65° E.[2]
Verified working — step 1
B (70 N) and C (70 S) share meridian 65 E, on opposite sides of the equator.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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