ECZ 2024 · GCE Paper 2 · Question 12 — Earth Geometry
The points P(80°N, 50°W), Q(80°N, 80°E), R(50°N, 80°E) and T(50°N, 50°W) are on the surface of the earth [π = 3.142 and R = 6 370km]. A frustum of a cone has base radius 2cm, top radius r cm and height 3.6cm [π = 3.142].
(a(i)) Draw a sketch to represent the above information.[2]
Verified working — step 1
Draw a circle to represent the sphere (Earth) with N and S poles marked, the equator, and the Greenwich Meridian (0°) drawn vertically. Draw two parallels of latitude: 80°N (near the North Pole) and 50°N (further from the pole). Draw two meridians: 50°W (to the left of Greenwich…(a(ii)(a)) Calculate the distance QR along longitude 80°E in kilometres.[2]
Verified working — step 1
QR lies along the meridian 80°E, so it is a great circle arc.(a(ii)(b)) Calculate the distance RT along latitude 50°N in kilometres.[2]
Verified working — step 1
RT lies along the parallel of latitude 50°N (a small circle).(b(i)) Calculate the value of r if the height of the cone from which the frustum was made was 6cm.[2]
Verified working — step 1
Let the full cone have base radius R = 2 cm and height H = 6 cm.(b(ii)) Calculate the volume of the frustum.[4]
Verified working — step 1
Volume of frustum = Volume of full cone - Volume of small cone removedThe 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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