I asked this question yesterday, and I'm trying to understand it since I got the wrong answer - please explain:

You need to make a soda can with a volume of 29 cubic inches.

Find the surface area. calculate the following:
a) How much material is needed if the can's radius is 1 inch?

I figured it this way:

Let the height be h
volume = π r²•h
29 = π (1²) • h
h = 29/π

So πr² • 2 + 2π • 29/π

2π + 58 = 64.28 in²

but person who helps me gets it this way:

Let the height be h
volume = π r²h
π (1²)h = 29
h = π /29

the surface area are
= 2 π r²+ 2 π rh
= 2 π (1) + 2 π (1)( π /29)
= 6.96 in²

Can anyone help me and tell me which is correct? I think the problem may
be that I get the volume 29/╥

intead of ╥/29

π (1²)h = 29

If you divide both sides by π, you get:

h = 29/π

To find the surface area of a soda can, you need to consider both the top and bottom circular faces as well as the curved portion that wraps around the can.

First, let's determine the correct volume of the soda can:
- The volume of a cylinder (such as a soda can) is given by the formula V = πr²h, where r is the radius and h is the height.
- Given that the volume is 29 cubic inches, we can solve for h: 29 = π(1²)h.
- This simplifies to h = 29/π, which is the correct height.

Now, let's calculate the surface area using the correct volume and diameter:
- The surface area of a soda can is given by the formula A = 2πr² + 2πrh.
- Since the radius is 1 inch, the diameter is 2 inches.
- Therefore, the correct formula becomes A = 2π(1)² + 2π(1)(29/π).
- Simplifying this equation, we get A = 2π + 58, which is equal to 64.28 square inches.

So, based on the correct calculations, the surface area of the soda can with a radius of 1 inch is approximately 64.28 square inches. Your initial calculation of 6.96 square inches seems incorrect.