Formula for Total Surface Area

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Homework Help Overview

The problem involves calculating the total surface area of a cylindrical pipe with given inner and outer diameters. The original poster seeks to determine the value of k in the expression for total surface area represented as k*PI.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the components of the surface area calculation, including the inner and outer surfaces and the ends of the cylinder. There is confusion regarding which areas need to be included and how to account for the annular shape of the ends.

Discussion Status

Some participants have provided guidance on breaking down the surface area into its components, while others are questioning the necessity of certain areas in the calculation. There is an ongoing exploration of the correct formulas and interpretations of the problem setup.

Contextual Notes

Participants express uncertainty about the terminology used, such as "packed," and the implications of the two diameters provided. There is a focus on ensuring all relevant areas are considered in the total surface area calculation.

zak100
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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.
 
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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.
 
zak100 said:
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.

asc.png


You need only the area of green part, The red part is not required.
 
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.
 
zak100 said:
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.
 
@zak100, you need to calculate the total surface area: the area of the two ends, the inner surface area, and the outer surface area.
zak100 said:
If the total surface area (inside and out, including the ends) is k*PI
Drawing a picture of the pipe will be helpful.
 
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).
 
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.
 
  • #10
zak100 said:
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.

zak100 said:
I don't know about the word "packed".
The pipe is not filled with anything (other than, say, air).
 
  • #11
Areas.jpg
 
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  • #12
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.
 
  • #13
zak100 said:
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.
 
  • #14
Sorry. Picture C is an orange circle.

Zulfi.
 
  • #15
zak100 said:
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?
 
  • #16
Hi,
Thanks for your guidance.

Area of annulus = Area of larger circle - area of smaller circle
Okay i would try the remaining calculation.
Zulfi.
 
  • #17
zak100 said:
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.
 
  • #18
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.
 
  • #19
zak100 said:
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.
 

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