Question

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=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).
Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+12πr . 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 6 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)=

Part c: If the surface area is 175 square inches, then what is the radius r ? In other words, evaluate r(175) . Round your answer to 2 decimal places.

The radius is ? inches if the surface area is 175 square inches

Answer 1

The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function.

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 given as

A=2πr² + 2πrh

Part A: Assume that the height of your cylinder is 6 inches.

Consider A as a function of r, so we can write that as

A(r) = 2πr² + 12πr

Then the domain of A(r) will be (0, ∞).

Part B: Continue to assume that the height of your cylinder is 6 inches.

Then the inverse function to A(r) will be

r = 2π[A(r)]² + 12πA(r)

Part C: If the surface area is 175 square inches.

Then the radius will be

                    175 = 2πr² + 12πr

r² + 6r – 27.866 = 0

                        r = 3.07, -9.07

Then the radius will be 3.07 inches.

More about the function link is given below.

brainly.com/question/5245372

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