SOLUTION: A steel plant has to fill an order from an automobile manufacturer for 100,000 steel ball bearings ½ inches in diameter. What is the total weight of the metal required to fill this

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Question 344567: A steel plant has to fill an order from an automobile manufacturer for 100,000 steel ball bearings ½ inches in diameter. What is the total weight of the metal required to fill this order, if steel weighs 480 lb per cu. ft?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Each bearing is a sphere.
The volume of a sphere is,
V=%284%2F3%29%28pi%29R%5E3
V=%284%2F3%29%28pi%29%280.5%29%5E3
V=0.5236cu.inches
For 100,000 bearings, the volume would be,
V%5Bt%5D=1000000%280.5236%29=52359 cu. inches
There are 12 inches in 1 foot and 12%5E3 cubic inches in 1 cubic ft.
V%5Bt%5D=52359%2F12%5E3=52359%2F1728=30.3cubic feet
To find the weight, multiply the volume by the density,
m=rho%2AV%5Bt%5D=480%2A30.3=14544 lbs.