Question

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

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