find the weight in pounds of 100 steel balls each 2.50 inches in diameter

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Request for Question Clarification by scriptor-ga on 06 Nov 2002 12:55 PST

Dear gonzales,

What is the given weight of steel per cubic inch for this question?
The weight of steel varies, so without knowing the value valid in this
case the question can't be answered.

Regards,
Scriptor

Hi, gonzalez-ga:

Steel does come in various "alloys" of iron and other metals, and
density varies with temperature to an extent.  However stainless steel
is a convenient mass density reference material:

http://ts.nist.gov/ts/htdocs/230/233/calibrations/mechanical/mass.htm

having a density of 8.0 grams per cubic centimeter, or 

(0.002204585537918871) * 8 / (0.393701)^3 = 0.289 pounds per cubic
inch

We then calculate the volume of steel balls you describe:

100 * (4pi/3) * (2.5)^3 = 6544.985 cubic inches

and multiply by the density above:

6544.985 * 0.289 = 1891.5 pounds

To find the weight (grams to pounds) and length (centimeters to
inches) conversion factors, I used the online conversion calculators
found at:

http://www.onlineconversion.com/

regards, mathtalk-ga

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Clarification of Answer by mathtalk-ga on 08 Nov 2002 17:07 PST

See Bushman-ga's correction to my answer.  I treated the dimension as
a radius which you gave as a diameter, overestimating the result by a
factor of 8.

-- mathtalk-ga

Nice try mathtalk, but not quite right!  Volume of a sphere is
4/3*pi*r^3 NOT 4/3*pi*d^3.  Sorry, your answer is off by a factor of
8.

Hi, bushman-ga

Thanks for the correction.  I misread the dimension.

1891.5/8 = 236.4375 pounds

Not quite as neat a number, but accurate!

regards, mathtalk-ga