Height of Cylindrical Tank

[Guest]

A cylindrical water heater has the following description:

20 inches circumference.

Volume is 50 gallons.

Determine height.


My attempt:

Let H = height

Diameter = circumference / pi

20 / 3.1416 = 6.3336 / 2 = 3.1668

Volume = pi x r^2 x H

3.1416 x 3.1668 x 3.1668 x H = 50


31.505H = 50

31.505H / 31.505 = 50 / 31.505

H = 1.587

Where am I correct?



Converting the circumference to feet: 20 / 12 = 1.6666 ft.


Radius = 1.6666 / 3.1416 = 0.5304 / 2 = 0.2652


Volume = 3.1416 x 0.2652 x 0.2652 x 1.57 = 0.346 cu. ft.


0.346 x 7.48 = 2.588 gal.

Where am I correct?

[Guest]

Please reply. Thanks.

[Guest]

The 50 gallons is the capacity of the cylinder in gallons.
You need to convert this into the dimensions you are working in...either cu.inches OR cu. feet.
Then divide by the area of the end to find height

[Guest]

50 x 231 = 11550 cu . in.

3.1416 x 3.1668 x 3.1668 = 31.505 sq. ft.

11550 / 31.505 = 366.60 in. = 30.55 ft.

Correct ?

[Guest]

.either cu.inches OR cu. feet.

You are working in "both inches and feet " and getting mixed up

work in one or the other

[Guest]

R = 20 / 3.1416 = 6.366 / 2 = 3.183 in.

3.1416 x 3.183 x 3.183 = 31.82 sq. in.

31.82H = 11550

31.82H / 31.82 = 11550 / 31.82 = H = 362.97 in.

??

[Guest]

yes, correct............

If you take Pi as 22/7 and work it out as one expression for H.....most of it will cancel leaving.....
7 x H = 11 x 231
giving H = 363 inches OR 30 feet 3 inches

[Guest]

Thanks again.

One comment:

I have a 40 gal. water heater and the height is nowhere near 30 ft. The 50 gal. was being placed in a renovated vintage camper trailer. I am fairly sure the dimensions were correct.


Could I have misheard the dimensions or the person giving them was mistaken in giving the diameter instead of circumference ? The information was on a TV show about renovating / restoring vintage campers / trailers.

[Guest]

Yes,...... 20 inches diameter would make a lot of a difference..... that is 10 inch radius

100 x Pi x H = 50 x 231

H = 50 x 231 / 314.2 = 36.76 inches = 3 feet approx

It still sounds big for a campervan....50 gallon at 10 lbs per gallon = 500 lbs .....1/4 of a ton weight...???

[Guest]

Sounds big to me also.

Thanks again.

[Guest]

Just for info follow-up:

Here is a link to another example:

http://americanwaterheater.com/resident ... /e6n-30lb/

Diameter = 22"

Volume = pi x r^2 x h

3.1416 x 11 x 11 x 30 = 11404.008 cu. in.

11404 / 231 = 49.367 = 49 gal.

I don't understand.

[Guest]

Please respond. Thanks again.

[Guest]

What do you not understand

Original question was a 20 inch diameter having capacity of 50 gallon had height 36.76 inches as you worked out.

Now this question has diameter 22 inches and height 30 inches and capacity of 49 gallon as you worked out.

Both answers seem reasonable and mathematically correct.

[Guest]

This is what I don't understand:

2nd: 3.1416 x 11 x 11 = 380.1336 = 380 sq. in. (area of base)

30 gal. x 231 = 6930 cu. in. (volume)

6930 / 380 = 18.23 in. = 1.519 ft. (height)


The description says height is 30 in. = 2.5 ft.

[Guest]

Please reply. Thanks.

[Guest]

Please respond.

[Guest]

What do you not understand

Original question was a 20 inch diameter having capacity of 50 gallon had height 36.76 inches as you worked out.

Now this question has diameter 22 inches and height 30 inches and capacity of 49 gallon as you worked out.

Both answers seem reasonable and mathematically correct.



This is what I don't understand:.......This is a different problem...?????

2nd: 3.1416 x 11 x 11 = 380.1336 = 380 sq. in. (area of base)

30 gal. x 231 = 6930 cu. in. (volume)

6930 / 380 = 18.23 in. = 1.519 ft. (height)

This is for a 30 gallon tank, 22 inches diameter, and 18 inches OR 1.5 feet in height

...........It was the 49 / 50 gallon tank that was 2.5 feet in height

[Guest]

" This is a different problem...????? " This is the second one (from the link).

The description says 30 gal., 30 in. in height, 22 in. in diameter. (" Tech Specs" : Dimensions)


You said I worked out the height as 1.519 ft., capacity as 49 gal. mathematically.

The description says height 30 in. which is 2.5 ft.

[Guest]

Maybe it is standing on legs OR a frame which is approx 1 foot high...???

[Guest]

" Maybe it is standing on legs OR a frame which is approx 1 foot high...??? "

That could be a possibility. I didn't think about that.

Thanks again.