Diameter - Tank

[Guest]

A cylindrical tank is 28' high and capacity of 38,000 cu. ft. Determine diameter of tank.

Formula I located :

Sq. root Capacity x 231 / Depth x .7854 = Diameter

28 x 12 = 336 in.

336 x 231 = 77616

336 * .7854 = 263.89

77616 / 263.89 = 294.12

Sq. rt. 294.12 = 17.1499 = 17 in. = Diameter


Volume of tank - pi x r^2 x height

3.1416 x 8.574 x 8.574 x 336 = 77599.17 = 77599 cu. in. = 44.90 = 45 cu. ft.

Where did I make the error(s) ?

[Guest]

Capacity divided by height equals the area of the circular section.

(Pi x (diameter)^2) / 4 OR Pi x (Radius)^2 = Area of circular section

[Guest]

38000 / 28 = 1357.142 = 1357

3.1416 x 1357 x 1357 = 5785096.17 = 5785096

How do I proceed ?

[Guest]

38000 / 28 = 1357.142 = 1357.......as stated in my last post this is the AREA of the circular section of the tank

3.1416 x 1357 x 1357 = 5785096.17 = 5785096......what you have done here is Pi x AREA x AREA = something..?????? did you not read my last post.????

It clearly stated this as copied below.....
(Pi x (diameter)^2) / 4 OR Pi x (Radius)^2 = Area of circular section
You have to make use of this information to find the radius or the diameter..........

[Guest]

1357 / 3.1416 = 431.95 = 432 area / pi

Sq. rt. of 432 = 20.784

Volume - 3.1416 x 20.784 x 20.784 = 1357

1357 x 28 = 37996 = 38000 cu. ft.

??

[Guest]

1357 / 3.1416 = 431.95 = 432 .....This is the radius squared........

Sq. rt. of 432 = 20.784 ......so you took sq root to get radius...OK


Were you wanting to check the calc in reverse..???
Why did you write Volume - 3.1416 etc....
Volume - 3.1416 x 20.784 x 20.784 = 1357

3.1416 x 20.784 x 20.784 = 1357 ......This is Pi x radius x radius again so you have found the area
1357 x 28 = 37996 = 38000 cu. ft. .....and the area x height is the volume.

You have not found the diameter yet.

[Guest]

I am not sure how even with formulas you provided.

[Guest]

I will attempt:

Area = pi x r^2

1357 = 3.1416 x r^2

1357 / 3.1416 = pi ^r2 / pi

431.945 = 432 = r^2

sq. rt. 432 = sq. rt. r^2

20.784 = r

20.784 x 2 = 41.568 = d

3.1416 x 20.784 x 20.784 x 28 = 37998.56 = 38000 cu. ft.

Not sure.

[Guest]

20.784 x 2 = 41.568 = d

Yes, thats it.

[Guest]

Thanks.

A follow-up question:

With the diameter being determined, if I wanted to find the volume with the diameter, how could I use the same formula?

[Guest]

20.784 = r

20.784 x 2 = 41.568 = d = diameter

Volume = Pi x[ r^2] x height ...... but..... r = d/2 ...so r^2 = (d x d) / (2 x 2) = d^2 / 4

Volume Pi x [d^2 / 4] x height

3.1416 x [(41.568 x 41.568) / 4] x 28 = 37998.56 = 38000 cu. ft.

[Guest]

Thanks again.