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StepMaths Mock Paper 1 · Q12

Paper 1Geometry

A right circular cone has base radius RR and height HH, where R<HR<H. A cylinder is inscribed in the cone in such a way that the curved surface of the cone is tangential to the cylinder as shown in the diagram below. Find the maximum volume of the cylinder in terms of RR and HH only. Diagram for question 12

A13πR2H\dfrac13\pi R^2H
BπH2R2(H−R)\dfrac{\pi H^2R}{2(H-R)}
C2R3\dfrac{2R}3
D4πR2H9\dfrac{4\pi R^2H}9
E4πR2H27\dfrac{4\pi R^2H}{27}

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