ECZ 2019 · GCE Paper 2 · Question 10 — Earth Geometry

Question from ECZ 2019 · GCE Paper 2 · Question 10

(a) The diagram below shows a frustum TQRS of a cone. [Take π as 3.142] Given that US = 3 cm, UV = 10 cm and RV = 8 cm, calculate its volume.[6]

Verified working — step 1

Extend the frustum to the full cone: similar triangles give Rr = Hh, so 83 = Hh.

(b) The points K, L and M are on the surface of the earth as shown in the diagram below. [Take π as 3.142 and R = 6 370 km]

(b(i)) Find the difference in longitude between points K and L.[2]

Verified working — step 1

K is at 30 W and L at 60 E, o…

(b(ii)) Find, in kilometres, the distance

(b(ii)(a)) LM,[2]

Verified working — step 1

L(50 N) and M(45 S) share meridian 60 E, so measure along the meridian.

(b(ii)(b)) KL.[2]

Verified working — step 1

K and L share latitude 50 N with a longitude difference of 90°.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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