Three part question I am struggling with the math

Question

Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function or r, so we can write that as A(r)=2π*r2+12π*r. What is the domain of A(r)? In other words, for which values of r is A(r) defined?

Part b: Write the r as the function of A. This is the inverse functions to A(r), i.e to turn A as a function of r into, as a function of A.

Part c: If the surface area is 250 square inches, then what is the radius r? In other words, evaluate r(250). Round your answer 2 decimal places.

Answer 1

Domain is r≥0, cylinder cannot have negative radius.

have

2πr²+12πr-A=0

r₁,r₂=[(-12π)/4π]±√(144π²+8Aπ)/4π,,,, quadradic roots

since r is positive if A>0, only one root

r₁=[(-12π)/4π]+√(144π²+8Aπ)/4π

plug in A to find r