ECZ 2017 · GCE Paper 2 · Question 12 — Earth Geometry
A cone ABC has the small cone AXY cut off leaving frustum BCXY: EX = 4cm (radius of small cone), DB = 12cm (radius of base), DE = 15cm [π = 3.142]. Earth-geometry points: P(80°N, 10°E), Q(80°N, 70°E), R(85°S, 70°E), S(85°S, 10°E) [R = 3437 nm].
(a(i)) Calculate the height AE of the smaller cone AXY.[2]
Verified working — step 1
Since AXY ~ ABC (similar cones), AEAD= EXDB(a(ii)) Calculate the volume of XBCY, the shape that remained.[4]
Verified working — step 1
Height of full cone AD = AE + ED = 7.5 + 15 = 22.5 cm, radius DB = 12 cm(b(i)) Show P, Q, R and S on a clearly labelled sketch of the surface of the earth.[2]
Verified working — step 1
Draw a circle to represent the earth with the North Pole (N) at the top and South Pole (S) at the bottom. Mark the equator as a horizontal line through the centre.(b(ii)(a)) Find in nautical miles the distance QR along the longitude.[2]
Verified working — step 1
Q and R lie on the same meridian (70°E), so distance QR is measured along a great circle (longitude).(b(ii)(b)) Find in nautical miles the circumference of the circle of latitude 85°S.[2]
Verified working — step 1
Circumference of a circle of latitude θ = 360 × 60 × cos θ (in nm)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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