There’s this 3 worded problem that I need a solution on.

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 325 square inches, then what is the radius r? In other words, evaluate r(325). Round your answer 2 decimal places.

Answer 1

(a) The domain of A(r) is all nonnegative real numbers; that is, r>0. r cannot be negative because r represents a length in space irrespective of direction.

(b) Let A = 2π r² + 12π r. Then 2π r² + 12π r - A = 0, so that by the quadratic formula we have

r = (-12π + √(144π² +8πA) ) / 4π

(c) If A = 325, then r(325) = (-12π + √(144π² +8π(325)) ) / 4π ≈ 4.79 inches.

Hope this helps!