Formula for Total Surface Area

[zak100]

Homework Statement

A 5-foot long cylindrical pipe has an inner diameter of 6 feet and an outer diameter of 8 feet. If the total surface area (inside and out, including the ends) is k*PI , what is the value of k?

Homework Equations

In my view the formula should be:
2* PI * radius * h + 2*PI * radius * radius

The Attempt at a Solution

I am confused with the formula. I made the attempt but found the answer wrong because of wrong formula.

Some body please guide me.
Zulfi.

 

[phyzguy]

Try writing down the area of the inside surface, the area of the outside surface, and the area of the two ends. Write down each of these formulas separately and then try to add them up.

 

[Buffu]

In my view the formula should be:
2* PI * radius * h + 2*PI * radius * radius

2*PI *radius *radius won't come in the formula because the cylinder given is not "packed" from top and bottom.
You need to subtract inner area and outer area.

You need only the area of green part, The red part is not required.

 

[zak100]

Hi,
Thanks for your response. Maybe because its a cylindrical pipe you are saying that we don't need: 2*PI * radius * radius
inner r= 3 ft: inner surface area = 2 * PI * 3 * 5 = 30 PI
outter r= 4 ft : outer Surface area = 2 * PI * radius * radius = 2 * PI * 4 * 5 = 40 PI

<
You need to subtract inner area and outer area.>
Why has he given 2 diamters if we have to calculate only outer area??
Some body please guide me.
Zulfi.

 

[Buffu]

Why has he given 2 diamters if we have to calculate only outer area??

Who told you that we only need to calculate outer area.
We need to calculate the the green area(see the picture in my previous post) for the top and the bottom of the cylinder.
For the lateral surface area we need $2 \times 2\pi rh$, multiplying it by 2 because the inner surface area will also count.

 

[Mark44]

@zak100, you need to calculate the total surface area: the area of the two ends, the inner surface area, and the outer surface area.

If the total surface area (inside and out, including the ends) is k*PI

Drawing a picture of the pipe will be helpful.

 

[zak100]

Hi,

I got above picture from internet.
What is meant by
<the cylinder given is not "packed" from top and bottom>
I have calculated the inner & outer surface area as you said.
<You need to subtract inner area and outer area.>
But subtraction is not giving me the correct answer.
Zulfi.Reference https://www.physicsforums.com/threads/formula-for-total-surface-area.896653/

 

[phyzguy]

Your Post #4 gives the inner and outer areas of the pipe. I think these are correct. Now please write down what you calculated for the areas of the two ends, and what you calculated for the total area of the pipe (inside+outside+end1+end2).

 

[zak100]

Hi,
In my opinion, area of end would be 2* PI * r * r but you are saying:
<
2*PI *radius *radius won't come in the formula because the cylinder given is not "packed" from top and bottom>

Plz guide me the formula for the area of end of cylinder.
I don't know about the word "packed".
Zulfi.

 

[Mark44]

In my opinion, area of end would be 2* PI * r * r

No.
Buffu's drawing in post #3 shows the end of the pipe. You need to calculate the area in green, not both areas (green and red). The outer radius of the pipe is 4 ft. and the inner radius is 3 ft. There are two ends to the pipe that must be included in the total surface area.

I don't know about the word "packed".

The pipe is not filled with anything (other than, say, air).

 

[Nidum]

 

[zak100]

Hi,
<There are two ends to the pipe that must be included in the total surface area.>
Do you mean the front circular end and the back circular end?
That's why i was using the formula 2 Pi *r * r for two ends of pipe.

Zulfi.

 

[Mark44]

Hi,
<There are two ends to the pipe that must be included in the total surface area.>
Do you mean the front circular end and the back circular end?
That's why i was using the formula 2 Pi *r * r for two ends of pipe.

The ends are NOT circular!
The ends look like C in the image that Nidum posted.

 

[zak100]

Sorry. Picture C is an orange circle.

Zulfi.

 

[Mark44]

Sorry. Picture C is an orange circle.

No it is not. A and B are disks. C is an annulus (a ring). What is the area of an annulus?

 

[zak100]

Hi,
Thanks for your guidance.

Area of annulus = Area of larger circle - area of smaller circle
Okay i would try the remaining calculation.
Zulfi.

 

[Mark44]

Area of annulus = Area of larger circle - area of smaller circle

YES!
This is what the images in posts 3, 7, and 11 are all about.

 

[zak100]

Hi,
Area of Larger circle = PI * 4 * 4= 16 Pi
Area of Smaller circle = PI * 3 *3 = 9 PI
Area of Annulus = 16 PI - 9 PI= 7PI
There are two Annulus. So the total surface area is:
40PI + 30 PI + 7PI + 7 PI
= 84 PI
So k = 84
Thanks everybody.
Zulfi.

 

[Buffu]

Hi,
Area of Larger circle = PI * 4 * 4= 16 Pi
Area of Smaller circle = PI * 3 *3 = 9 PI
Area of Annulus = 16 PI - 9 PI= 7PI
There are two Annulus. So the total surface area is:
40PI + 30 PI + 7PI + 7 PI
= 84 PI
So k = 84
Thanks everybody.
Zulfi.

You should read your textbook again and go through example problems.