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).

Question

Mathematics

Lilyana Mendoza

29 September, 04:52

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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Answers (1)

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Blevins · Answer 1

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)

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

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).