Question

The surface area of a soup can represents the total area of the can's exterior and may be found by the formula S.A. = 2πrh + 2πr2. A soup company designing its own cans wants to determine the height of its cans with a given surface area and radius.

Help the company by solving the surface area formula for h.

Answer 1

So which part of the right hand side of the equation contains the h?

Answer 2

2pirh

Answer 3

yes :) So from the last problem we did, we learned to ut all the stuff that doesn't contain what you're trying to solve for onto the other side of the equation, right? So can you show me how you would put everything that doesnt have "h" in it to the other side with the appropriate sign?

Answer 4

and btw, pretend the "SA" is actually like a "0" so when you move the stuff onto the other side, don't include it in your problem :)

Answer 5

subtracting 2pir2 on both sides ?

Answer 6

You got it! :)

Answer 7

\[-2\pi r^2= 2\pi rh\]

Answer 8

Now what else can we do so we get "h" by itself?

Answer 9

divide ?

Answer 10

mmhmm, but divide what by what?

Answer 11

both sides by 2pirh ?

Answer 12

Wait,no no, remember,you are solving for h, if you divide with it, you cannot solve for it!

Answer 13

oh so -2pir^2

Answer 14

We currently have \[-2\pi r^2=2\pi rh\] in order to get "h" by itself, we need to divide by something, but we're not going to touch the h, because that is what we are solving for. what other things can we divide by to get H all by itself?

Answer 15

2pir ?

Answer 16

yessir :)

Answer 17

So we will have \[-\frac{ 2\pi r^2 }{ 2\pi r }=h\]correct?

Answer 18

yes

Answer 19

do we have to do something else ?

Answer 20

Yes :) Now you can reduce the function of h. Notice how there are like terms (similar terms such as 2, pi and r) in both the numerator and denominator? We can eliminate those as well

Answer 21

what do we get ?

Answer 22

We have \[(-\frac{ 2 }{ 2 })(\frac{ \pi }{ \pi })(\frac{ r^2 }{ r })=h\] so we can reduce them all.

Answer 23

i divide each ?

Answer 24

Yep!

Answer 25

pi divided by pi would be ?????? 1 ?

Answer 26

You got it :D

Answer 27

and how about the 2's?

Answer 28

-2 / 2 = -1

Answer 29

mmhmm. and the r's?

Answer 30

r^2

Answer 31

\[\frac{ r^2 }{ r }= r ^{2-1}\] can you reduce that?

Answer 32

r

Answer 33

And now we put all the values together :)

Answer 34

-11r ?

Answer 35

\[(-1)(1)(r)=h\]

Answer 36

thats the answer ? cuz i have different answer choices

Answer 37

Lets see. I'll rework the problem out here for you to check your work?

Answer 38

\[h = \frac{ 2\pi r }{ S.A. + 2\pi r }\]

\[h = \frac{ 2\pi r }{ S.A. - 2\pi r }\]

\[h = \frac{ S.A. + 2\pi r }{ 2\pi r }\]

\[h = \frac{ S.A. - 2\pi r }{ 2 \pi r }\]

Answer 39

Or wait... I think we had to include SA as part of the answer. but no worries, it's all going to be the same except now we're going to have SA as part of the answer.

Answer 40

yes! :)

Answer 41

all the other steps we had done were correct, we just have to reinclude SA

Answer 42

So i will work out the problem too, and you can check your work with mine?

Answer 43

ok :)

Answer 44

\[SA=2\pi rh+2\pi r^2\]\[SA-2\pi r^2=2\pi rh\]\[\frac{ SA-2\pi r^2 }{ 2\pi r }=h\]

Answer 45

Now i believe we cannot eliminate any variables because there are no common terms that are shared with SA. So that is our answer. Before when we did not include SA as part of our answer, we were able to reduce all the terms because they shared stuff in common

Answer 46

so which one on top would it be ?

Answer 47

I am sorry, i made a mistake in not including SA into solving this problem.

Answer 48

its ok... i sent u my choices above ? i still dont know which one since none of my choices have ^2

Answer 49

Hmm... it's not matching any of these answers. let's see \[h=\frac{ SA }{ 2\pi r }-\frac{ 2\pi r^2 }{ 2\pi r}\] this would reduce down to \[h=\frac{ SA }{ 2\pi r }-r\]

Answer 50

the closest thing is choice D, but that's missing a square over the r

the other choices don't even come close to the true answer of \[h = \frac{ S.A. - 2\pi r^2 }{ 2 \pi r }\]

which is what Jhannybean got above

Answer 51

so my guess is that there's a typo

Answer 52

is there a typo ? here is my question

Answer 53

\[h=\frac{S.A-2\pi r^2}{2\pi r}\]

Answer 54

ill just put D :p

Answer 55

There's no answer, lol

Answer 56

hmmm