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Maths Made Easy TMUA Paper 1 · Q18

Paper 1Geometry

A pyramid has a square base of side length ss and four equilateral triangular faces. A sphere of radius rr is inscribed in the pyramid, touching all five faces. A second sphere of radius RR is circumscribed about the pyramid, passing through all five vertices.

Find the ratio of the volume of the circumscribed sphere to the inscribed sphere.

A6+1036+10\sqrt3
B8+438+4\sqrt3
C10+6310+6\sqrt3
D12+5312+5\sqrt3
E16+2316+2\sqrt3

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