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7 November, 17:58

A hollow cylinder, open at one end, is constructed of thin sheet metal. The total external surface area of the cylinder is 192pi cm^2. The cylinder has a radius of r cm and a height of h cm.

(i) express h in terms of r and show that the volume, Vcm^3 of the cylinder is given by

V=pi/2 (192r-r^3).

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  1. 7 November, 20:10
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    S A = r² π + 2 r π h

    192 π = r² π + 2 r π h / : π

    192 = r² + 2 r h

    2 r h = 192 - r²

    h = (192 - r²) / 2 r

    V = r² π h = r² π ((192 - r²) / 2 r) =

    = π / 2 (192 r - r³)
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