Lyons Boone
08/10/2023 · High School
A closed, right circular cylinder of base radius r cm and height h cm has a volume of \( 54 \pi \mathrm{~cm}^{3} \). Show that \( S \), the total surface area of the cylinder, is given by \[ S=\frac{108 \pi}{r}+2 \pi r^{2} \text {. } \] Hence find the radius and height which make the surface area a minimum.
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The radius and height that minimize the surface area of the cylinder are \( r = 3 \text{ cm} \) and \( h = 6 \text{ cm} \).
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