Weight - Tank - Solution / Explanation

[Guest]

An open tank has the following dimensions :

Length - 2 ft.
Width - 2 ft.
Depth - 1.5 ft.
Thickness - 1/8 in.

The tank is made of lead.
Lead weighs approx. .42 lbs. per cu. in.


Determine weight of tank.

Volume = length x width x height or depth

Solution provided with problem :

External dimensions of tank - 24.25 in. in length, 24.25 in. in width, 18.125 in. deep.

External volume - 24.25 x 24.25 x 18.125 cu. in.

Volume - 600 x 18 = 12000 cu. in. *

Enclosed volume - 24 x 24 x 18 = 12000 cu. in.

External volume - 10650 cu. in.

Enclosed volume - 10370 cu. in.

Volume occupied by lead - 10650 - 10370 = 280 cu. in. **

280 x .42 (cu. in. of lead) = 117.6 = 120 lbs.


My solution:

24.25 x 24.25 x 18 = 10585.125 = 10585 cu. in.

10585 x .42 (cu. in. of lead) = 4445.7 lbs.

Which is correct ?

* What is the 600 ?

** Why is the enclosed volume subtracted from the external volume to obtain volume occupied by lead ? The tank is completely made of lead.

[Guest]

Take internal size as 2 ft x 2 ft x 1.5 ft OR 24 ins x 24 ins x 18 ins. = 10368 cu. ins = volume of empty space inside the lead shell.

Add on thickness of 1/8 ins

Then external size is 24.25 x 24.25 x 18.125 open tank....no lid. = 10658.6 cu. ins = external volume as if a solid cube.

Volume of lead in sides or shell of tank = 10658.6 - 10368 = 290.6 cu ins.

weight of tank = 290.6 x 0.42 = 122.05 lbs.


OR by calc. the volume of lead in sides + base

Sides = 96.5 x 18 x 1/8 = 217.125 cu. ins

base = 24.5 x 24.5 x 1/8 = 73.508 cu. ins

Total volume of lead = 217.125 + 73.508 = 290.633

Weight of tank = 290.633 x 0.42 = 122.07 lbs.

[Guest]

What is the 600 ?

[Guest]

Volume - 600 x 18 = 12000 cu. in. *

Enclosed volume - 24 x 24 x 18 = 12000 cu. in.

Both these calculations are wrong, they are in your calculation, not mine

[Guest]

I suppose the person who wrote the solution provided with problem miscalculated also.


Also, is the internal size subtracted from the external size due to the empty space (just air) ?

[Guest]

The external dimensions give volume of a whole solid cube of that size.
The internal dimensions give the volume of a whole solid cube of that size

The difference between them is the volume of the shell between them.

It does not matter if the inner cube is filled with water, air, sand or any other material.

It is similar to distances between towns etc

If it is 100 miles between town A and town B.
And 150 miles between town town A and town C in the same direction.

Then it is 50 miles between town B and town C

[Guest]

Thanks.