SOLUTION: Trying to help my son figure out surface area of a cylinder. What is the surface area if the radius is 4 ft. and the height is 21 ft. Do you do as follows: 2(3.14)(8)+ 2(3.14)(

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Question 882262: Trying to help my son figure out surface area of a cylinder.
What is the surface area if the radius is 4 ft. and the height is 21 ft.
Do you do as follows:
2(3.14)(8)+ 2(3.14)(4)(21) = 577.76.
Not sure that is correct. Where are we going wrong?
Tx for your help!!!! Final tomorrow :)
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39615) (Show Source):
You can put this solution on YOUR website!
Not sure what level since you did not say.

Cutting the open cylinder along its length and unroll, you find the unrolled length corresponds to the circumference of the rolled form; and the length along which the cylinder was cut is "height" of this unrolled form. You also have the two disc surfaces.

You have then two terms to be added for the total surface area:
, the sum of the unrollable curved tube and the two circular discs. You know h=21, and r=4, so you can replace the variables with them.

We have Commutative Property of Addition, so you can also say .

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Here's where you made the mistake. You computed when it *should* have been

<--- Exact Surface Area (in terms of )

<--- Approximate Surface Area (using the approximation )

Note: to get a better approximation, use more digits of .

Another Note: the units of the final answer are in square feet.