Question

Alex designed the model of a cylindrical water tank to be installed in a park. The model has a radius of 4 cm and a height of 12 cm. The dimensions of the actual water tanks that will be installed in the park are 5 times larger than the model. The total surface area of the actual water tanks, rounded to the nearest whole number, is _________ cm2.

Answer 1

can i get steps on how you solve it please

Answer 2

First, do you know how to get the surface area of a cylinder?

Answer 3

no i do not

Answer 4

Ok, that's just a formula:
\[SA_{cylinder}=top~area+bottom~area+side~area\]so:[\[SA_{cylinder}=2(area~of~top) + 2(perimeter~of~top)*height\]

Answer 5

Finding the area of the top and bottom is easy: \[A_{top~or~bottom}=\pi r^2\]The area of the side will be the circumference times the height:\[A_{side}=(2 \pi r)(height)\]

Answer 6

Put that all together to get: \[SA_{cylinder}=2\pi r^2 + 2\pi rh\]

Answer 7

Are you with me so far?

Answer 8

sorta kinda....

Answer 9

What part is confusing you at the moment? We'll get to the calculation next but that's the easy part.

Answer 10

o' ok i got it now.....i just had to re-read.
i was looking at the surface area formula and what u wrote then saw the area formual and was like huh? then i got farther down and saw that you put it together so surface formula and area formula together which is how u got S.A.= 2pir2 + 2pirh

Answer 11

Ok, great. Using the last equation above, calculate the SA of the model cylinder and tell me what you get please.

Answer 12

ok hang on a sec.

Answer 13

2(3.14)4cubed is....100.48
2(3.14)4x12 is 301.44 which equals 401.92?

Answer 14

Here:\[SA=2\pi(4^2)+2\pi(4)(12) \approx402\]

Answer 15

That's in square inches of course.

Answer 16

If you're good with that, let's do the last part.

Answer 17

was my math correct though?

Answer 18

Your math is correct but in the first line you through me for a loop because you say cubed and not squared :)

Answer 19

o sorry lol :)

Answer 20

So now you know the formula and how to apply it. The last part of the question states that the dimensions of the actual tanks are 5 times larger. So what do you think you need to do?

Answer 21

do i take 401.92 and multiply it by 5?

Answer 22

No..that would be a silly mistake. All you need to do is multiply the dimensions by 5 and THEN apply the formula again.

Answer 23

ok so i multiply 100.48 by 5 and 301.44 by 5?

Answer 24

No...that's equivalent to what I said not to do :). Multiply the dimensions given in the problem by 5...and then do the formula.

Answer 25

so if im understanding corrrectly...im going to multiply 4(radius) by 5 the (height) 12 by 5 and then put those in the formula like before

Answer 26

Exactly

Answer 27

oki doki hang on

Answer 28

2512
946521.6
which equals 948133.6?

Answer 29

I got 10053in^2 (rounded to the nearest whole number). Try it again...and I'll check my answer.

Answer 30

I got 10048 this time but only because I used 3.14 instead of the longer version of pi.

Answer 31

\[2(3.14)20^2+2(3.14)(20)(60)=10048\]

Answer 32

ok this is what im doing...
2(3.14)20 squared=2512
2(3.14) 20 times 60 = 7536 which equals 10048

Answer 33

ok i see what i did....i used the 20squared in the second half of the equation lol

Answer 34

insead of just 20

Answer 35

Glad you found the mistake! Ok, so that's the final answer.

Note that if you had just multiple 402x5 you would have came up with 2010...which is far different than 10,000. The reason you can't just multiply your first answer time 5 is because there are exponents in the formula. If those weren't there, it would have worked.

Answer 36

You didn't even need to do the first answer...but we did it so you could understand the formula.

Answer 37

ohhh ok well i totaly understand it now...thank you sooo much you helped me alot :)

Answer 38

cool, good luck :)

Answer 39

hang on wait....if it says use 22/7 for pi would it still be the same? or how would i do that

Answer 40

@Shane_B
if i had to use 22/7 for pi instead of 3.14 would i end with 10057.142857?

Answer 41

That's correct

Answer 42

ok cool thanks (: