ECZ 2016 · GCE Paper 2 · Question 12 — Earth Geometry
Question from ECZ 2016 · GCE Paper 2 · Question 12
(a) The diagram below shows the cross-section of a circular metal disc of radius 14 mm. The disc has a central hole which is a square of side 4 mm. [π = 3.142]
(a(i)) Calculate the shaded area in mm2.[3]
Verified working — step 1
Area of the circle = π r2 = 3.142 × 142 = 615.832 mm2.(a(ii)) Given that the thickness of the disc is 5 mm, calculate in mm3 the amount of materials required to make 20 such discs.[3]
Verified working — step 1
Volume of one disc = shaded area x thickness.(b) In the diagram below, A(65° N, 5° E), B(65° N, 45° W) and C are three points on the surface of the model of the earth and O is the centre of the model. The point C, due south of A, is such that angle AOC = 82°. [π = 3.142, R = 3 437 nm]
(b(i)) State the longitude of A.[1]
Verified working — step 1
Read the meridian on whic…(b(ii)) Calculate the latitude of C.[1]
Verified working — step 1
C is due south of A on the same meridian, so angle AOC is the difference in latitude.(b(iii)) Calculate, in nautical miles, the shortest distance
(b(iii)(a)) between A and C measured along the common longitude,[2]
Verified working — step 1
A and C share a meridian, so the distance runs along a great circle.(b(iii)(b)) between A and B measured along the circle of latitude.[2]
Verified working — step 1
A and B are both on latitude 65 N; longitude 5 E to 45 W spans 5 + 45 = 50°.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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