ECZ 2011 · O-Level Paper 2 · Question 7 — Earth Geometry
Question from ECZ 2011 · O-Level Paper 2 · Question 7
(a) The shaded part of the diagram below is that of a path of a car windscreen wiper. The wiper rotates through 120° about O. (Take π to be 227) Given that OA = OB = 30 cm, AC = BD = 40 cm, calculate
(a(i)) the perimeter of the sector OCD correct to 1 decimal place,[3]
Verified working — step 1
OC = OD = 30 + 40 = 70 cm.(a(ii)) the area of the shaded region correct to 1 decimal place.[3]
Verified working — step 1
The shaded region is the large sector minus the small one.(b) P and Q are points on the surface of the earth situated on the same parallel of latitude 70° N as shown below. The longitudes of P and Q are 25° W and 15° E respectively. A and B are two points on the equator such that A is due south of P and B is due south of Q. (π = 3.142, R = 3437 nm)
(b(i)) State the position of the point Q.[1]
Verified working — step 1
Read the position as (latitude, longitude).(b(ii)) Find the distance between A and B.[2]
Verified working — step 1
A and B lie on the equator, so the longitude difference is 25 + 15 = 40°.(b(iii)) Calculate the circumference of the small circle at 70°N.[1]
Verified working — step 1
The circle of latitude 70 N has radius R cos 70.(b(iv)) Find the distance along the parallel of latitude between P and Q, correct to 2 decimal places.[2]
Verified working — step 1
P and Q share latitude 70 N with a longitude difference of 40°.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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