ECZ 2012 · O-Level Paper 2 · Question 9 — Earth Geometry
Question from ECZ 2012 · O-Level Paper 2 · Question 9
(a) The diagram below shows a wire model of the earth. The circle of latitude in the north is 50° N and the circle of latitude in the south is 60° S. A and C are on longitude 55° W while B and D are on longitude 50° E. (Take π = 3.142 and R = 3437 nm)
(a(i)) Write the positions, using longitudes and latitudes, of the points A and D.[2]
Verified working — step 1
Read each position as (latitude, longitude).(a(ii)) Calculate the difference in longitudes between A and B.[1]
Verified working — step 1
A is at 55 W and B at 50 E, on opposite sides of the prime meridian.(a(iii)) Given that the time at town D is 09 20 hours, what would be the time at town C?[1]
Verified working — step 1
C is at 55 W and D at 50 E, a difference of 105°.(a(iv)) Calculate the distance BD along the longitude 50° E in nautical miles.[2]
Verified working — step 1
B is at 50 N and D at 60 S on the same meridian, so the latitudes add.(b) A cylindrical geyser of radius 21 cm and length 50 cm is placed with its curved surface on a horizontal ground. It is filled partially with water and the segment ABY in the diagram shows the cross section of water in the geyser. O is the centre of the circular end of the geyser, Y is vertically below O and angle AOB = 120°. (Take π = 227). Calculate
(b(i)) the curved surface area of the geyser,[2]
Verified working — step 1
Curved surface area of a cylinder = 2 π r l.(b(ii)) the volume of water in the geyser correct to the nearest whole number.[4]
Verified working — step 1
Y lies on the 120° arc, so the water forms the MINOR segment cut off by chord AB.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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