is this how you set up and solve the problem?

Question

the question is a cylindrical can of pringles has a lateral surface area of 156 π cm^2. If the radius of the can is 6 cm, find the height ?

1. the formula is s=2πrh.
2. plug it in, 156=2(3.14)6h
3. then after that you multiply the 3.14 by 2 to make it 6.28. you subtract it by 156 and then you divide it by 6h to get your answer right?

if not how?

Answer 1

LSA = 156π cm^2
r = 6 cm

LSA = 2πrh
156 π = 2 π * 6h
156 = 12h (The π on each side cancel out to give 2*6h on RHS)
h = 156/12
h = 13 cm

There's no need to approximate π. In the question the LSA is given without the value of π considered. And in the answer the π cancels itself out. So there isn't any need for values. Your step 2 in the question is wrong by the way. This is what you put:
156 = 2*π*6*h ( I made the 3.14 into π)

This is the correct step
156π = 2*π*6*h

You forgot the π in the LHS. You must right it that way as that is the LSA. Ignoring π will result in an approxiamte and totally wrong answer. I suppose that's where you went wrong.

Answer 2

surface area = 2πrh
h = S / 2πr
h = 156π / (2 * 6 *π)
where..
π / π = 1
then
h = 156 / 12
h = 13 cm

Answer 3

This is what you do: Multiply 3.14 times 2 (6.28). Then you multiply that by six (which is 37.68). Divide 156 by 37.68 and you'll get the value for h (which is about 4.14)

Answer 4

Surface Area of a Cylinder = 2 pi r^2 + 2 pi r h

156 pi cm^2 = 490 cm^2 = .049 m ^2

.049 = 2 (3.14) (.06)^2 + 2 (3.14) (.06) h

h = .07 m