Question

Find the surface area of the cylinder with a radius of 9 inches and a height of 11 inches in terms of pi

Answer 1

@Qwertty123

Answer 2

@DanJS

Answer 3

Let's start with the area of the two circles at the bottom

Answer 4

Have you considered the circumference of the base?

Answer 5

Using \[\pi r^2\]
What is the area of one of those circles?

Answer 6

i dont know

Answer 7

Afterwards, keep in mind that the vertical surface of a cylinder unfolds into a rectangle,
So therefore the circumference of the base is the length and 11 is the height

Answer 8

i thought i used radius not circumfrence

Answer 9

Well plug it in @sunshine0829
It is \[\pi(9)^2\]

Answer 10

3.14 (9) ^2

Answer 11

Well let's keep off of circumference for now
Find the area of the circle

Answer 12

Yup so what is that?

Answer 13

275.4

Answer 14

Ok so there are 2 circles, and that is the area of one circle
So what should we do to get the area of both circles

Answer 15

multiply 275,4 times 2??

Answer 16

Yep
And that is?

Answer 17

550.8

Answer 18

Ok keep that number aside
Now as I said earlier the other vertical surface of a cylinder unfolds into a rectangle
Like this

Answer 19

huh

Answer 20

Do you see how that works?

Answer 21

yes but how does that relate to the answer

Answer 22

Well think of it this way
Doesn't the length of the rectangle equal the circumference of the circle?

Answer 23

sure

Answer 24

helpppp

Answer 25

Because the rectangle wraps around the circle perfectly
I don't want you just blowing off this explanation without understanding k?
think of it as if you wrap a string around a circle, If it fits perfectly then it's the same length as the circle right?

Answer 26

yes

Answer 27

@Brill

Answer 28

Ok so same concept with the rectangle, if it fits perfectly then it's length is the same as the circumference of the circle and it's height is given
So how would you solve for the area of the rectangle?

Answer 29

no

Answer 30

Umm
That isn't a yes or no question

Answer 31

Just saying

Answer 32

i dont know

Answer 33

Well what's the circumference of the circle?

Answer 34

9

Answer 35

Umm no that's the radius
Circumference is 2(pi)r

Answer 36

225

Answer 37

@Brill

Answer 38

No @sunshine0829

Answer 39

ugh

Answer 40

you know what nvm. i dont want your help since you wanna be rude

Answer 41

Sorry it's not rude
I'm just saying please put in effort because you just popped out the answer you gave me earlier instead of just doing 2(pi)9

Answer 42

But anyway you would do the circumference multiplied by the height to get the area of the rectangle then you would add in the area of the two circles we found earlier to get your final answer