The height of the cylinder is 4 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. Letrbe the radius of the top of the can and lethbe the height.The surface area of the cylinder,A, isA=2r2+2rh(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 is4inches.ConsiderAas a function ofr, so we can write that asA(r)=2r2+8r. 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 is4

inches. Write the radiusr as a function ofA. This isthe inverse function toA(r), i.e to turnAas a function ofrinto.ras a function ofA.

Hints:

• To calculate an inverse function, you need to solve forr. Here you would start withA=2r2+8r. This equationis the same as2r2+8rA=0 which is a quadratic equation in the variabler and you can solve that using the quadratic formula.

Part c: If the surface area is225 square inches, then what is the radiusr? In other words, evaluater(225).Round your answer to 2 decimal places.

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 is225square inches.

My answers are attached...they are showing as incorrect in my textbook but I am unsure of what I've done wrong. Since b is coming up incorrect I was getting 77.29 for C, but that also is incorrect.

Part A: r is the radius, the radius cannot be o or negative. The domain of A (r) = (0,00) The Quadratic Part B: Assuming the height (h) = 4. Formula Alv ) = 27152 + Sirs ax " to x + c = 0 where ate x : - b = \\ b2 . yac 2a 0 - 2752 + 8+1r - A a = 2Tr b= 8 mr C =- A X = r r = - 841 = (8TT) 2- 4(2 TT ) ( A ) 2( 2 TT ) 1 = 2 (- 4 ) = 64 +2 - 8THA) 2 ( 2 7 ) r = - 2TK - V647 2 + 8TIA r = - 2 # \\u4712 + 8 TTA sincer cannot be negative r = - 2 + Vu4712 + 8 TA