## Description

The height of the cylinder is 8 inches.

We'll be analyzing the surface area of a round cylinder - in other words the amount of material needed to "make a can".

A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let

Part a: Assume that the height of your cylinder is

Part b: Continue to assume that the height of your cylinder is

Hints:

- To calculate an inverse function, you need to solve for
r . Here you would start withA=2πr2+16πr . This equation is the same as2πr2+16πr−A=0 which is a quadratic equation in the variabler , and you can solve that using the quadratic formula. - If you want to type in
3π+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.

Part c: If the surface area is

Hint: To compute a numeric square root such as

- Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
- Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
- Use a calculator

The radius is inches if the surface area is

I will need a step-by- explanation plus the answers. Let me know if you need anything else.

## Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.Both the files are exactly the same content-wise.Thanks

Module Two Discussion Question

The height of the cylinder is 8 inches.

We'll be analyzing the surface area of a round cylinder - in other words the amount of material

needed to "make a can".

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 =

2𝜋𝑟 2 + 2𝜋𝑟ℎ (it's two circles for the top and bottom plus a rolled up rectangle for the side).

Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r, so we can

write that as 𝐴(𝑟) = 2𝜋𝑟 2 + 16𝜋𝑟. What is the domain of A(r)? In other words, for which values

of r is A(r) defined?

Part a: Radius r can have any value which is greater than zero, so the domain of A(r):

(𝟎, ∞)

Part b: Continue to assume that the height of your cylinder is 8 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)=

Hints:

•

To calculate an inverse function, you need to solve for r. Here you would start

with A=2πr2+16...