The height of the cylinder is 8 inches. We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can". A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A=2πr2+2πrh (it's two circles for the top and bottom plus a rolled up rectangle for the side). Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+16πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A(r), i.e to turn A as a function of r into. r as a function of A. r(A)= Hints: To calculate an inverse function, you need to solve for r. Here you would start with A=2πr2+16πr. This equation is the same as 2πr2+16πr−A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula. If you want to type in 3π+1x+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit. Part c: If the surface area is 275 square inches, then what is the rardius r? In other words, evaluate r(275). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as 17.3−−−−√, you could Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3) Use a browser to connect to the Internet and type in sqrt(17.3) into a search field Use a calculator The radius is inches if the surface area is 275 square inches.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 9P: A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can,...

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The height of the cylinder is 8 inches.

We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can".

A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A=2πr2+2πrh (it's two circles for the top and bottom plus a rolled up rectangle for the side).

Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+16πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined?

Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A(r), i.e to turn A as a function of r into. r as a function of A.

r(A)=

Hints:

To calculate an inverse function, you need to solve for r. Here you would start with A=2πr2+16πr. This equation is the same as 2πr2+16πr−A=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula.
If you want to type in 3π+1x+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.

Part c: If the surface area is 275 square inches, then what is the rardius r? In other words, evaluate r(275). Round your answer to 2 decimal places.

Hint: To compute a numeric square root such as 17.3−−−−√, you could

Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
Use a calculator

The radius is inches if the surface area is 275 square inches.

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