Question

please help
Find the total surface area of the figure shown here when D = 50 cm, d = 40 cm, and h = 55 cm.

Answer 1

the given choices :

A) 4592 π square centimeters
B) 5213 π square centimeters
C) 5328 π square centimeters
D) 5400 π square centimeters

Answer 2

I used this rule the surface area of cylinder is =
\[2\Pi r ^{2} + 2 \Pi r h\]

Answer 3

but the answer was not included in the choices , of course I did something wrong.
any help please?

Answer 4

Jody, You can't use that rule because there is a hole in the cylinder, but try to find the circumference on the top outer cylinder circle

Answer 5

ok I'll find it now

Answer 6

I'll tell you why later

Answer 7

so 2 pi r = 2 *3.14 * 25 = 157 cm
so this is the circum. of the outer top circle

Answer 8

ok

Answer 9

Ok so let's say that you cut the cylinder clean into a rectangular prism. the length would be 157 cm

Answer 10

ok so L=157 cm

Answer 11

the width [or thickness] is 5 cm, and also I was wrong on the length. you also need the inner circumference, then add 157 to the inner circumference, then divide by 2

Answer 12

ok so for now the W=5 cm

Answer 13

yes

Answer 14

now the length is: [inner cir+outer cir]/2

Answer 15

inner cirum = 2 pi r = 2*3.14*20 = 125.6
after adding it to the 157 cm
so the whole circum. will be 282.6 cm

Answer 16

good. now divide by 2 to get 141.3

Answer 17

so 282.6 /2 = 141.3 cm

Answer 18

that is the length

Answer 19

the height is already known

Answer 20

so L= 141.3 cm
w = 5 cm

Answer 21

Yep!

Answer 22

yes h = 55 cm
L= 141.3 cm
W= 5 cm

Answer 23

now calculate
[l*w+l*h+h*w]*2

Answer 24

ok

Answer 25

17506

Answer 26

then ?

Answer 27

Hmm Im stumped here.
@mathmale
Can u help mathmale?

Answer 28

yes this is where I got so confused , I couldn't find the answer in any of the given choices

Answer 29

@mathmale can you please help us here?

Answer 30

ill msg him

Answer 31

I msged him

Answer 32

I see you've already spent a lot of time on this problem, and have explored various means of solving it. Please describe where ... and how ... you'd like for me to begin.

Before you do anything else, explain in your own words what the goal of this problem is.

Answer 33

The goal is to find the surface area of a cylinder, shown at the top.

Answer 34

we have the dimensions, but we aren't very sure what went wrong

Answer 35

the way I read this problem, you have a figure, which is not a cylinder, but rather is a solid with a vertical hole through its center. Do y ou agree or disagree?

Answer 36

I agree with you

Answer 37

OK. So let's now list all the surfaces we have:

1) two washers of outside diameter D and inside diameter of d, and ...
2) an outer surface, which, if "unwound" from the solid, would be a rectangle, and ...
3) an inner surface which, if "unwould" ... would also be a rectangle.

Answer 38

Question #1 for you both: Given that the outside diameter is D, what is the area of the outside cylindrical surface?

Answer 39

Well, using 3.14 as Pi, it is 1963.495408

Answer 40

That is with counting the hole's space

Answer 41

Let's please just concentrate on the area of the outside cylindrical surface.
What formula are you using to calculate that?

Answer 42

A=Pi*r^2 [area of circle is Pi times the radius squared]

Answer 43

We're not talking about the same thing. By "outside cylindrical surface" I mean ONLY the outside of this cylindrical solid (no area of a circle here, at least, not yet).

Hint: What is the circumference of a circle of diameter D?

Answer 44

Ohh... the circumference is 157.0796327

Answer 45

Now we're in agreement.
How tall is the figure?

Answer 46

It is 55 cm tall

Answer 47

Right. So, now, what is the area of the outside cylindrical surface (just THAT one surface)? By the way, where is @jody999?

Answer 48

Ok 55*157.1 [rounding] is 8640.5 is the outer area of the figure.
P.S. I msg @jody999 so shell come soon

Answer 49

I'm really glad you're interested and involved here...but this was originally Jody's problem. Your result, 8640 square units, is correct for the area of the outside surface of this cylindrical object.

Please guide Jody through the process of finding the surface area of the cylindrical hole. (Help her do it herself, referring to your and my discussion.)

Answer 50

Ok, and Thanks!

Answer 51

Message me when you're ready to resume. I may not be available immediately, but if you need help I will provide it ... today. And thank YOU.

Answer 52

Wait.. that's too high... it's not one of her ABC choices

Answer 53

A) 4592 π square centimeters
B) 5213 π square centimeters
C) 5328 π square centimeters
D) 5400 π square centimeters

Answer 54

@Dbzfan836 sorry my laptop battery died

Answer 55

I'm reading the posts now

Answer 56

Jody, even mathmale couldn't find it out.

Answer 57

yes I can see this :(
what do you think about this I will email my instructor and ask him for an explanation, right ?
so I'll close the question for now and I will reply back when I got something
agree?

Answer 58

Yeah, I agree

Answer 59

Gtg

Answer 60

ok thanks a lot for your help with this one , I really appreciate it :)
@Dbzfan836