I cannot figure this out can somebody please help me?

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=2r2+2rh (it's two circles for the top and bottom plus a rolled up rectangle for the side).

A round cylinder with a circle top and base with radius r and a height of h

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)=2r2+16r. What is the domain of A(r)? In other words, for which values of r is A(r) defined?

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.

r(A)=

To calculate an inverse function, you need to solve for r. Here you would start with A=2r2+16r. This equation is the same as 2r2+16rA=0 which is a quadratic equation in the variable r, and you can solve that using the quadratic formula.

If you want to type in 3+1x+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.

Part c: If the surface area is 325 square inches, then what is the rardius r? In other words, evaluate r(325). Round your answer to 2 decimal places.

Hint: To compute a numeric square root such as 17.3, 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 calculator

The radius is

Number

inches if the surface area is 325 square inches.

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Part a: Can we have a can that is -6 feet across and -10 feet tall?

Part b: Start with the function for A and substitute h=8:

A(r)=2r2+2rh=2r2+16r.

Then "solve for r" in this equation. You'll get a radical function.

Part c: This is easy once you've down Part b!