ECZ 2015 · O-Level Paper 2 · Question 11 — Earth Geometry

Question from ECZ 2015 · O-Level Paper 2 · Question 11

(a) A, B, C and D are points on the surface of the earth as shown in the diagram below.

(a(i)) Using latitudes and longitudes, write the positions of the points A and B.[2]

Verified working — step 1

Read each position as (latitude, longitude) from the diagram.

(a(ii)) Find the difference in longitude between points C and D.[1]

Verified working — step 1

C is on 31 E and D on 81 E, both east of Greenwich.

(a(iii)) Calculate the distance CD in nautical miles [π = 3.142 and R = 3437 nm].[2]

Verified working — step 1

C and D share latitude 80 S, so measure along that parallel.

(a(iv)) Given that the local time at D is 13 05 hours, find the time at C.[1]

Verified working — step 1

Each degree of longitude is 4 minutes of time.

(b) A cylindrical water tank at Mwaiseni Lodge has diameter of 200 cm and height 250 cm as shown below. Taking π to be 3.142, find

(b(i)) the total surface area of the tank if it is closed,[3]

Verified working — step 1

Radius r = 2002 = 100 cm.

(b(ii)) the number of litres of water the tank can hold.[3]

Verified working — step 1

Volume = π r² h = 3.142 × 100² × 250

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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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