Hi, Kindly assist with the below (please include working, I have...

Hi,

Kindly assist with the below (please include working, I have attached screenshot of problem as well):

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: Find the inverse function to A(r). Your answer should look like r="some expression involving A".

 

r(A)=

 

Part c: If the surface area is 175

 square inches, then what is the radius r? In other words, evaluate r(175). Round your answer to 2 decimal places.

 

The radius is  inches if the surface area is 175 ______ square inches.

Screenshot below for clarity:

Image transcription text

' 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 7- be the radius of the top of the can and let h be the height. The surface area of the cylinder, A, is A = 271'7'2 + Zarh (it's two circles for the top and bottom plus a rolled up rectangle for the side). r= radius Areas = 1: 1'2: h = height Area = hi23rr) fi :3 Circumference 2m Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so w can write that as A (r) = 2 7W2 + 16 at". What is the domain of A (7')? In other words, for whic values of r is A (1') defined? Part b: Find the inverse fimction to A (1'). Your answer should look like 7' ="some expressio involving A". 7-(A): Em Hints: 0 To calculate an inverse function, you need to solve for 'r. 2 + 161m This equation is the same a - Here you could start with A = 2 m" 2 «7'2 + 16 m1 — A = 0. Do you recognize this as a quadratic equatio 0.32 + In: + c = 0 where the variable a: is r? The coefficients would be 2 1r for a, 16 1r fo 6, and —A for c. 0 You can solve for 7' using the quadratic formula even though the constant term c is a symb here. Part (:2 If the surface area is 175 square inches, then what is the radius r? In other words, evalua 7' (17 5). Round your answer to 2 decimal places. Hint: To compute a numeric square root such as \f 17 .3, you could 0 Use a spreadsheet such as Microsofi Excel or OpenOffice Cale and type in =sqrt(l 7.3) 0 Use a browser to connect to the Internet and type in sqrt(l7.3) into a search field 0 Use a calculator The radius is Number inches if the surface area is 175 square inches.

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