height of a cylinder(round can) is 8". what is the domain of A(r)

Question

This question has three parts and I am having a hard time at a starting point

Part a: the formula is A(r)=2*Pi^2+16*Pi*r How would I find the domain of A(r)?

Part b: finding the r as a function of A r(A) with the height being 8"

Part c: How to find the radius when given 175 square inches

If someone could please explain and help me with a starting point!

Answer 1

To begin with, A(r) is a function representing the surface area of a cylinder of height = 8" and the radius = r.

A(r) = 2πr² + 16πr

r must be a positive number (you can't have a radius of negative length), so the domain of A(r) is r > 0. (There is no upper limit to what r can be.)

Solving for r in terms of A is an odd question, and a little challenging but possible using completing the square:

A/(2π) = r² + 8r

A/(2π) + 16 = r² + 8r + 16

A/(2π) + 16 = (r + 4)²

r = √(A/(2π) + 16) - 4

So when A = 175, r = √(175/(2π) + 16) - 4 , which is one ugly, irrational number.