ECZ 2022 · O-Level Paper 2 · Question 11 — Earth Geometry

The diagram shows the points P(20 degrees N, 80 degrees E), Q(40 degrees S, 80 degrees E) and R(40 degrees S, 30 degrees E) on the surface of the earth. [Take pi as 3.142 and R = 6370 km]

(a(i)) The diagram shows the points P(20 degrees N, 80 degrees E), Q(40 degrees S, 80 degrees E) and R(40 degrees S, 30 degrees E). Find the difference in longitudes between points R and Q.[2]

Diagram for part (a(i))

Verified working — step 1

R is on longitude 30 degrees E an…

(a(ii)) Calculate the distance PQ in kilometres.[2]

Diagram for part (a(ii))

Verified working — step 1

P (20 degrees N) and Q (40 degrees S) both lie on longitude 80 degrees E, so PQ runs along a great circle.

(a(iii)) Find the length of the circle of latitude 40 degrees S in kilometres.[2]

Diagram for part (a(iii))

Verified working — step 1

A circle of latitude has radius R cos 40.

(b(i)) The diagram shows a bin BCDE made by cutting off the smaller cone ADE from the cone ABC. Given that AF = 9 cm, BG = 8 cm, EF = 3 cm and GF = h cm, calculate the value of h.[2]

Diagram for part (b(i))

Verified working — step 1

Cones ADE and ABC are similar, so AGAF= BGEF.

(b(ii)) Calculate the volume of the bin BCDE.[4]

Diagram for part (b(ii))

Verified working — step 1

Volume of bin = volume of cone ABC - volume of cone ADE

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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