We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can". The height of the cylinder is 8 inches. 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)=2πr^2+16 πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined? I believe the answer to this part is "All real numbers" Part B: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of 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. For this part nothing I have written is working. Any help will be much appreciated. Part c: If the surface area is 200 square inches, then what is the rardius r? In other words, evaluate r(200). Round your answer to 2 decimal places. I have Part C answer correctly it says at 2.92 inches if the surface area is 200 square inches.
We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can".
The height of the cylinder is 8 inches.
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)=2πr^2+16 πr. What is the domain of A(r)? In other words, for which values of r is A(r) defined?
I believe the answer to this part is "All real numbers"
Part B: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of 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.
For this part nothing I have written is working. Any help will be much appreciated.
Part c: If the surface area is 200 square inches, then what is the rardius r? In other words, evaluate r(200). Round your answer to 2 decimal places.
I have Part C answer correctly it says at 2.92 inches if the surface area is 200 square inches.
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