Question 187618
Volume of a Cylinder: {{{V=pi*r^2*h}}}



Solve for "h" to get {{{h=V/(pi*r^2)}}}



Note: in the volume of a cylinder formula, there are two independent variables "r" and "h" (ie they determine what V will turn out to be). Since we want the final function to be in terms of "r", this means that we need to eliminate "h".




Since we know that the volume is 100 cubic feet, this means that {{{V=100}}}. So plug that in to get {{{h=100/(pi*r^2)}}}



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Surface Area of a Cylinder: {{{SA=2*pi*r^2+2*pi*r*h}}}



{{{SA=2*pi*r^2+2*pi*r*(100/(pi*r^2))}}} Plug in {{{h=100/(pi*r^2)}}}. Notice how "h" is now gone (see above).



{{{SA=2*pi*r^2+(200*pi*r)/(pi*r^2))}}} Multiply



{{{SA=2*pi*r^2+(200*cross(pi*r))/(cross(pi)*r^cross(2)))}}} Cancel out the common terms.



{{{SA=2*pi*r^2+200/r}}} Simplify



So the function of radius r is {{{A(r)=2*pi*r^2+200/r}}}