ECZ 2025 · O-Level Paper 2 · Question 11 — Mensuration
Question from ECZ 2025 · O-Level Paper 2 · Question 11
(a) The diagram shows a bigger cone ABCDE with perpendicular height 18 cm from which a smaller cone BCD was cut to make a bucket ABDE. AE = 12 cm and CF = 6 cm. [Take π as 3.142] Calculate the
(a(i)) radius FD,[2]
Verified working — step 1
The bucket comes from cutting a small cone (height 6 cm) off the big cone (height 18 cm), so the two cones are SIMILAR.(a(ii)) volume of the bucket ABDE.[4]
Verified working — step 1
Bucket volume = big cone - small cone, with V = (13) π r2 h.(b) In the diagram, A, B, C and D are points on the surface of the earth. [Take π as 3.142 and R = 3 437 nm] Calculate the
(b(i)) length of the circle of latitude 52° N,[2]
Verified working — step 1
A circle of latitude at 52° N is smaller than the equator by the factor cos 52.(b(ii)) distance BC along the longitude 76° E,[2]
Verified working — step 1
B (52 N) and C (78 S) lie on the same meridian but on OPPOSITE sides of the equator.(b(iii)) distance DC along the circle of latitude 78° S.[2]
Verified working — step 1
D (43 W) and C (76 E) share the latitude circle 78 S, on opposite sides of the Greenwich meridian.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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