ECZ 2017 · GCE Paper 2 · Question 12 — Earth Geometry
Question from ECZ 2017 · GCE Paper 2 · Question 12
(a) The figure below is a cone ABC from which BCXY remained after the small cone AXY was cut off. [Take π as 3.142] Given that EX = 4 cm, DB = 12 cm and DE = 15 cm, calculate
(a(i)) the height AE, of the smaller cone AXY.[2]
Verified working — step 1
The cones AXY and ABC are similar, so AEAD = EXDB.(a(ii)) the volume of XBCY, the shape that remained.[4]
Verified working — step 1
Full cone: height AD = 7.5 + 15 = 22.5 cm, radius 12 cm.(b) P(80° N, 10° E), Q(80° N, 70° E), R(85° S, 70° E) and S(85° S, 10° E) are four points on the surface of the earth.
(b(i)) Show these points on a clearly labelled sketch of the surface of the earth.[2]
Verified working — step 1
Draw a circle for the earth with N at the top, S at the bottom and the equator across the middle.(b(ii)) Find in nautical miles
(b(ii)(a)) the distance QR along the longitude,[2]
Verified working — step 1
Q (80 N) and R (85 S) share meridian 70 E, so measure along the meridian.(b(ii)(b)) the circumference of the circle of latitude 85° S. [Take π as 3.142 and R = 3 437 nm][2]
Verified working — step 1
The circumference of a circle of latitude is 360 × 60 x cos(latitude) nautical miles.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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question