Question 14 — IGCSE 0580 Oct/Nov 2025 Paper 41
Cambridge IGCSE Mathematics 0580, Extended tier, calculator. Topic: Mensuration · Perimeter, Area and Volume. Worth 10 marks.
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Question text
14 A cube contains a solid metal sphere.
The sphere touches all the faces of the cube.
The side length of the cube is 8 cm.
256
(a) Show that the volume of the sphere is rcm3.
3
[1]
(b) Calculate the percentage of the cube that is not occupied by the sphere.
..............................................% [3]
(c) The density of the metal of the sphere is 7.86 g/cm3.
Calculate the mass of the sphere.
Give your answer in kilograms.
[Density = mass ' volume]
.............................................kg [2]
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* 0000800000009 *
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(d) The sphere is melted down and made into a solid cylinder with radius 3.1 cm.
Calculate the total surface area of the cylinder .
..........................................cm2 [4]
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