Length- Square

[Guest]

A cylindrical iron bar, 6 feet long and 2 inches in diameter, is formed into a square bar with a cross section of 2.25 square inches.

Determine length of new bar.

Thanks.

[Guest]

Determine length of new bar.

Round bar area ...... (3.142 / 4) x 2 x 2 = 3.142

Square bar area ..... 2.25 x 2.25 = 5.0625

Length of New Bar is .... (3.142 / 5.0625) x 6 = 3.724 feet

Ans....... 3.724 feet

[Guest]

My solution:

pi * r^2 * h = A x L
3.14 * 1^2 * 6 = 2.25 * L
18.84 = 2.25L
18.84/2.25 = 2.25/2.25
8.3733 = L

So volume of cylinder is not required ?

"Round bar area ...... (3.142 / 4) x 2 x 2 = 3.142"

Area of circle ?

[Guest]

Sorry my mistake ...... I see in the question that the square bar has a cross sectional area of 2.25 sq. inches.

So my original posting should have been..........

Determine length of new bar.

Round bar area ...... (3.142 / 4) x 2 x 2 = 3.142

Square bar area ..... 2.25

Length of New Bar is .... (3.142 / 2.25) x 6 = 8.379 feet

Ans....... 8.379 feet

I used Pi x d^2 / 4 for area and took Pi as 3.142 in above
..............................................

Or using Pi x r^2 for area of circle ..... as you do and taking Pi as 3.14

Round bar area ...... 3.14 x 1 x 1 = 3.14 sq. inches

Square bar area ..... 2.25 ... given this

Length of New Bar is .... (3.14 / 2.25) x 6 = 8.373 feet

Ans....... 8.373 feet

No the volume of the cylindrical bar is not really required ..... its just the ratio of the areas
Smaller area gives a longer bar......

[Guest]

"I used Pi x d^2 / 4 for area and took Pi as 3.142 in above"

I had forgotten that the diameter could be squared.

One question:

Did you divide by 4 because of squaring diameter ?

[Guest]

"I used Pi x d^2 / 4 for area and took Pi as 3.142 in above"

I had forgotten that the diameter could be squared.

One question:

Did you divide by 4 because of squaring diameter ?

--------------------------------
In the above I am just using the standard formula for the area of a circle.....
If we are given the diameter of the circle then tha area is (Pi x d^2 / 4)
Or in words Pi times d squared, divided by 4......
Or said the other way around.....Pi divided by 4, times d squared.....
Both are the same....Just rearranged and we are given the diameter so don't bother using the radius.

If we are working in terms of the circle radius.....the radius is half of the diameter = (d / 2).
and the standard formula for the area of a circle using radius is Pi x radius squared = Pi x r^2
Since r is d/2 then r^2 is (d/2)^2.....read as "d" over "2" all squared...to work this out you have to square the "d" and the "2" ... the top and bottom numbers of the fraction.
This gives (d^2) / (2^2) = (d^2) / (4) = (d^2) / 4.
So Pi x r^2 becomes Pi x (d^2) / 4 .... or written the other way around .... (Pi / 4) x d^2.

[Guest]

It is clear to me now. Thanks again.