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 theradius of the top of the can and let h be the height. The surface area of the cylinder, A,isA2rr + 2rrh (it's two circles for the top and bottom plus a rolled up rectangle for the side).r = radiusAreas = t r?h = heightArea = h(2rtr)Circumference2arPart a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we canwrite that as A (r) = 2 Tr2 + 16 Tr. What is the domain of A (r)? In other words, for which values ofr is A (r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a functionof 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 withA = 2 Tr + 16 tr. This equation is the same as 2 Tr2 + 16 Tr – A = 0 which is a quadratic-equation in the variable r, and you can solve that using the quadratic formula.3 T+1x+1more information in the Introduction to Mobius unit.• If you want to type inin Mobius, in text mode you can type in (3*pi+1)/(x+1). There isPart c: If the surface area is 175 square inches, then what is the rardius r? In other words, evaluater (175). Round your answer to 2 decimal places.Hint: To compute a numeric square root such as v17.3, 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 calculatorThe radius is Numberinches if the surface area is 175 square inches.

Question

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&#34;make a can&#34;.A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be theradius of the top of the can and let h be the height. The surface area of the cylinder, A,isA2rr + 2rrh (it's two circles for the top and bottom plus a rolled up rectangle for the side).r = radiusAreas = t r?h = heightArea = h(2rtr)Circumference2arPart a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we canwrite that as A (r) = 2 Tr2 + 16 Tr. What is the domain of A (r)? In other words, for which values ofr is A (r) defined? Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a functionof 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 withA = 2 Tr + 16 tr. This equation is the same as 2 Tr2 + 16 Tr – A = 0 which is a quadratic-equation in the variable r, and you can solve that using the quadratic formula.3 T+1x+1more information in the Introduction to Mobius unit.• If you want to type inin Mobius, in text mode you can type in (3*pi+1)/(x+1). There isPart c: If the surface area is 175 square inches, then what is the rardius r? In other words, evaluater (175). Round your answer to 2 decimal places.Hint: To compute a numeric square root such as v17.3, 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 calculatorThe radius is Numberinches if the surface area is 175 square inches.

Accepted Answer

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