# Formula for Total Surface Area

1. Dec 10, 2016

### zak100

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
In my view the formula should be:

3. The attempt at a solution
I am confused with the formula. I made the attempt but found the answer wrong because of wrong formula.

Zulfi.

2. Dec 10, 2016

### 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.

3. Dec 10, 2016

### Buffu

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.

4. Dec 11, 2016

### 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??
Zulfi.

5. Dec 11, 2016

### Buffu

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.

6. Dec 11, 2016

### Staff: Mentor

@zak100, you need to calculate the total surface area: the area of the two ends, the inner surface area, and the outer surface area.
Drawing a picture of the pipe will be helpful.

7. Dec 12, 2016

### zak100

8. Dec 12, 2016

### 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).

9. Dec 13, 2016

### 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.

10. Dec 13, 2016

### Staff: Mentor

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.

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

11. Dec 13, 2016

### Nidum

12. Dec 15, 2016

### 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.

13. Dec 15, 2016

### Staff: Mentor

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

14. Dec 15, 2016

### zak100

Sorry. Picture C is an orange circle.

Zulfi.

15. Dec 15, 2016

### Staff: Mentor

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

16. Dec 15, 2016

### zak100

Hi,

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

17. Dec 15, 2016

### Staff: Mentor

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

18. Dec 15, 2016

### 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.

19. Dec 15, 2016