ECZ 2024 · GCE Paper 2 · Question 12 — Earth Geometry

Question from ECZ 2024 · GCE Paper 2 · Question 12

(a) The points P(80° N, 50° W), Q(80° N, 80° E), R(50° N, 80° E) and T(50° N, 50° W) are on the surface of the earth. [π = 3.142 and R = 6 370 km]

(a(i)) Draw a sketch to represent the above information.[2]

Verified working — step 1

Sketch the sphere with the N and S poles, the equator and the Greenwich meridian.

(a(ii)) Calculate the distance

(a(ii)(a)) QR along longitude 80° E in kilometres,[2]

Verified working — step 1

QR runs along the meridian 80 E — a great circle.

(a(ii)(b)) RT along latitude 50° N in kilometres.[2]

Verified working — step 1

RT runs along latitude 50 N, from 80 E to 50 W — across Greenwich, so the longitudes ADD:

(b) The figure below is a frustum of a cone. The base radius is 2 cm, top radius is r cm and the height is 3.6 cm. [Take π as 3.142] Calculate the

(b(i)) value of r if the height of the cone from which the frustum was made was 6 cm,[2]

Verified working — step 1

The frustum (height 3.6 cm) came from a 6 cm cone, so the small cone cut off has height 6 - 3.6 = 2.4 cm.

(b(ii)) volume of the frustum.[4]

Verified working — step 1

Frustum = full cone - small cone, with V = (13) π r² h.

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.