Weight - Cast Iron Disc

[Guest]

A circular disc of cast iron is 7 ft. in diameter and 1 1/3 in. thick. Determine weight, with the knowledge that a plate 1 foot square and 1 inch thick weighs 37.5 lbs.

My attempt:

Area of circle - pi x radius squared.

3.1416 x 3.5 x 3.5 x 1.33 = 51.184 sq. in.

51.184 x 37.5 = 1919.4 lbs.

Where did I make the error(s) ? Thanks.

[Guest]

You've mixed up the units. Convert all lengths to either feet or to inches don't use both (otherwise you're asking for trouble).

However, having said this, your calculation should still give the right answer (fortunately the mixed up units cancel each other out in the right way). Your mistake is that you are rounding the value 1 1/3 too aggressively (you give it to 3 significant figures so you should expect your answer to be correct only to about 3 significant figures).
3.1416 x 3.5 x 3.5 x 1.33 x 37.5 = 1919.419425 lbs
3.1416 x 3.5 x 3.5 x 4/3 x 37.5 = 1924.23 lbs (correct to about 5 significant figures, because pi was given to that accuracy)

Hope this helped,

R. Baber.

[Guest]

That helped - thanks again.

[Guest]

I have a question:

Cast iron also weighs 450 lbs. per cu. ft. or .26 lbs. per cu. in. My question - could those units be used also to calculate the weight ? Thanks.

[Guest]

Yes. Which is precisely why it is always recommended that you change to consistent units throughout (mathematically you'll still get the right answer and there is less chance you'll make a mistake by accidentally mixing up the units later on in a long calculation).

However, be aware that the density 37.5 lbs per (inch x square foot) is 0.26041666... lbs per cubic inch, rounding to 0.26 will mean your answer will only be right to 3 significant figures.

Hope this helped,

R. Baber.

[Guest]

That helped also - thanks again.

[Guest]

"the density 37.5 lbs per (inch x square foot) is 0.26041666... lbs per cubic inch"

37.5 x 1 x 12 x 12 = 5400

37.5 x 0.08333 x 1 x 1 = 3.125

? ?

[Guest]

"per" translates to "divided by"
37.5 lbs per (inch x square foot) = 37.5 lbs / (inch x 12 inch x 12 inch)
= 37.5/(12 x 12) lbs/cubic inch
= 0.26... lbs/cubic inch

Hope this helped,

R. Baber.

[Guest]

Thanks - that helped.

[Guest]

Don't do the divisions too early in the solution.......if they don't work out even you end up with rounding errors.
The question was described using fractions and simple decimal numbers.....

One and a third inches is 4/3 x 12 = 1 / 9 of a foot.

So disc volume is (22/7) x (7 x 7 /4) x (1 /9) = (22 x 7 / 36) cu feet.

One sq foot by one inch thick is (1 /12) of a cu foot and this weighs 37.5 lbs.
So 1 cufoot weighs 12 x 37.5 lbs.

So the disc weight is (22 x 7 / 36) x (12 x 37.5) = 22 x 7 x 12.5 = 1925 lbs in weight

Answer = 1925 lbs.

[Guest]

Typo error

One and a third inches is 4/3 x 12 = 1 / 9 of a foot.
should be.....
One and a third inches is (4/3) / 12 = 1 / 9 of a foot.

[Guest]

"So disc volume is (22/7) x (7 x 7 /4) x (1 /9) = (22 x 7 / 36) cu feet."

(22/7) - I know this is pi.

(7 x 7 / 4) - I don't know how you obtained this.

(1/9) - I know this is the thickness.

Thanks.

[Guest]

(7 x 7 / 4) - I don't know how you obtained this.

The area of a circle is Pi x radius squared, that is (22/7) x (7/2) x (7/2) = (22/7) x (7 x 7) / 4.

This is the same as saying Area of circle is (Pi times diameter squared divided by 4)

and so is same as .... (22/7) x (7 x 7) / 4

[Guest]

I understand it now - Thanks.