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.Com
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
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) (Show Source): You can put this solution on YOUR website!
Your answer to part a is incorrect:
So
\ =\ \frac{V}{\pi r^2})
But 
is given to be 
So
\ =\ \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:
\ =\ 2\pi r^2\ +\ 2\pi rh)
\ =\ 2\pi r^2\ +\ 2\pi r\(\frac{21.7}{\pi r^2}\))
\ =\ 2\pi r^2\ +\ \frac{43.4}{r})
Part c: Find a common denominator, in this case, 
\ =\ \frac{2\pi r^3}{r}\ +\ \frac{43.4}{r})
\ =\ \frac{2\pi r^3\ +\ 43.4}{r})
(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
From
I > Ø
RELATED QUESTIONS
The diagram shows a cube of metal with a cylinder cut out of it. The formula for the... (answered by ikleyn)
A CYLINDER HAS A VOLUME OF 235.5 CUBIC INCHES. IF THE VALUE OF PI (3.14) USED TO... (answered by rapaljer)
if a cylinder has a radius of 12 inches and a volume of 13564.8 cubic inches. what is the (answered by math problem solving)
A cylinder has a base diameter of 18 inches and a height of 2 inches. What is its volume... (answered by MathLover1,ikleyn)
A cylinder has a volume of 46 cubic inches. If all the dimensions are multiplied by 2.5,... (answered by Boreal)
A right circular cylinder has a volume of 1000 cubic inches and a height of 8 inches,... (answered by checkley77)
what is the volume of a cylinder to the nearest tenth of a cubic inch with a radius of 7... (answered by stanbon)
An oblique cylinder has a radius of 9 centimeters and a volume of 486 cubic centimeters.... (answered by ankor@dixie-net.com)
if the volume of a cylinder is 45 cubic inches, find the volume of a sphere that has the... (answered by Alan3354)