Can someone please help me with this?

Hint: This is similar to Question 63 in Section 5.7 of our textbook. We covered this section in "1-4Reading and Participation Activities: Inverses and Radical Functions" in Module One. You can check some of your answers to parts b and c to make sure that you are on the right track.

The height of the cylinder is 6 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. Letr

be the radius of the top of the can and leth

be the height.The surface area of the cylinder,A, isA=2r^2 + 2h

(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 is6inches.ConsiderAas a function ofr, so we can write that asA(r) = 2r^2 + 12r. What is the domain ofA(r)? In other words, for which values ofrisA(r)defined?

Part b: Continue to assume thatthe height of your cylinder is6

inches. Write the radiusras a function ofA

. This isthe inverse function toA(r), i.e to turnAas a function ofrinto.ras a function ofA

.

r(A) = #enter answer#

Hints:

• To calculate an inverse function, you need to solve forr
• . Here you would start withA=2r
• 2
• +12r
• . This equationis the same as2r
• 2
• +12rA=0
• which is a quadratic equation in the variabler
• , and you can solve that using the quadratic formula.
• If you want to type in3+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 is325square inches, then what is the rardiusr? In other words, evaluater(325).Round your answer to 2 decimal places.

Hint: To compute a numeric square root such as17.3 squared, 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#enter answer# ifinches if the surface area is325

square inches.

Part a: Can we have a can that is -6 feet across and -10 feet tall?

Part b: Start with the function forAand substituteh=6:

A(r) = 2r^2 + 2rh = 2r^2 + 12r.

Then "solve for r" in this equation. You'll get a radical function.

Part c: This is easy once you've down Part b!