The radius of a right circular cylinder is 3.09 inches.
Volume can be given as the space occupied by the matter. The volume of the cylinder is given as:
Volume = πr²h
The total surface area (TSA) of a right circular cylinder is given as:
Area = 2πr(h + r)
The volume of the can is 60 cubic inch. Substituting the value:
60 = πr²h
h = 60/ πr²
Substituting the value for the height in the TSA formula:
[tex]\rm Area = 2\pi r (\frac{60}{\pi r^2} + r)\\\\Area = 2\pi r \;\times\;\frac{60}{\pi r^2}\;+\;2\pi r^2\\\\Area = \frac{240}{r^3}\;+\;4\pi[/tex]
This is the minimum surface area.
The value of the minimum area at the critical point is 0. Thereby:
[tex]\rm 0= \dfrac{240}{r^3}\;+\;4\pi\\\\r^2=\dfrac{120}{4\pi}\\\\r=3.09\;inches[/tex]
The radius of a right circular cylinder is 3.09 inches.
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