Surface Area r(A) of a cylinder

Question

Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we can write that as A(r)=2πr2+8πr. 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 4 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.

Part c: If the surface area is 200 square inches, then what is the radius r? In other words, evaluate r(200). Round your answer to 2 decimal places.

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Could someone break it down and explain to me on how to do this? please!

Answer 1

a) r ≥ 0, therefore, the domain of A is ≥ 0

b) You can use the quadratic formula to solve for r:in

2πr² + 8πr - A = 0

r = (-8π ± sqrt(64π²+8πA))/(4π) Since r>0 we can throw out the - option for the discriminant term:

r = -2 + sqrt(64π²+8πA)/(4π) - -2 + sqrt(4 +A/(2π))

c) Plug A into equation.

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