Official papers

Official 2016 Paper 1 · Q12

Paper 1Geometry

A right circular cylinder is contained within a sphere of radius 5 cm in such a way that the whole of the circumferences of both ends of the cylinder are in contact with the sphere.

The diagram shows a planar cross section through the centre of the sphere and cylinder. Diagram for question 12

Find, in cubic centimetres, the maximum possible volume of the cylinder.

A250π250\pi
B500π500\pi
C1000π1000\pi
D25033π\dfrac{250\sqrt{3}}{3}\pi
E50039π\dfrac{500\sqrt{3}}{9}\pi
F100039π\dfrac{1000\sqrt{3}}{9}\pi

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