SOLUTION: A standard beverage can has a volume of 21.7 cubic inches. a) Use formula for the volume of cylinder to write an equation that gives the height h of a standard beverage can in ter

Algebra ->  Rational-functions -> SOLUTION: A standard beverage can has a volume of 21.7 cubic inches. a) Use formula for the volume of cylinder to write an equation that gives the height h of a standard beverage can in ter      Log On


   

Question 1181950: A standard beverage can has a volume of 21.7 cubic inches.
a) Use formula for the volume of cylinder to write an equation that gives the height h of a standard beverage can in terms of its radius (I have solved this and I got h=square root (v/pi r)
b) Using expression for h from part (a) and the formula for the surface area of a cylinder, write an equation gives the surface area of the beverage can S in terms of only its radius r. (I got S=2pi+r%5E2+%2B+2pi-r+sqrt%28v%2Fpi+r%29
c) Rewrite the equation for S from part (b) as a quotient of 2 polynomials
d) Use graphing calculator to find the minimum value of S. What are the dimensions r and h of the can that use least amount of material?
e) Compare dimensions from part (d) with the actual beverages, which radius= 1.25 inches and height= 4.42 inches
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Your answer to part a is incorrect:



So



But is given to be

So



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

Part b isn't correct either:







Part c: Find a common denominator, in this case,







(Yes, is a monomial, but the monomials are a subset of the polynomials so this works)

.


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

My calculator said it, I believe it, that settles it

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