Question 1181950
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Your answer to part a is incorrect:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  V\ =\ \pi r^2h]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  h(r,V)\ =\ \frac{V}{\pi r^2}]


But *[tex \Large V] is given to be *[tex \Large 21.7\ in^3]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  h(r)\ =\ \frac{21.7}{\pi r^2}]


And the height will be in inches because you are dividing cubic inches by square inches.


Part b isn't correct either:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r,h)\ =\ 2\pi r^2\ +\ 2\pi rh]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ 2\pi r^2\ +\ 2\pi r\(\frac{21.7}{\pi r^2}\)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ 2\pi r^2\ +\ \frac{43.4}{r}]


Part c: Find a common denominator, in this case, *[tex \Large r]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ 2\pi r^2\ +\ \frac{43.4}{r}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ \frac{2\pi r^3}{r}\ +\ \frac{43.4}{r}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_T(r)\ =\ \frac{2\pi r^3\ +\ 43.4}{r}]


(Yes, *[tex \Large r] is a monomial, but the monomials are a subset of the polynomials so this works)


*[illustration SodaCanSurfaceArea.jpg].



The actual minimum radius for the minimum Total Surface Area is approximately 1.512 which results in a height of approximately 3.03 inches.

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

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