Question 1205074: A spherical piece of steel is 1/8" in diameter.
1). Determine volume.
2). Determine how many could be produced from 1 cu. in. of the material.
Check my calculations, please.
Sphere volume: 4/3 * pi * r^3
1.333 * 3.1416 * .0625^3
= .01021 cu. in. 1).
1 / .01021 = 97.84 = 98 2).
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
For the volume, the answer with your input numbers is 0.0010224 cubic inches.
Your calculation is incorrect.
For the number of pieces, the answer with your input numbers is 978.
Your calculation is incorrect.
If you take more decimal places for  , you will get slightly different values
for both the volume of a piece and the number of pieces, but it is just another story.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Part 1
Diameter = 1/8
Radius = 1/16 which is half the diameter
Volume = (4/3)*pi*(radius)^3
Volume = (4/3)*pi*(1/16)^3
Volume = 0.0010226538586
I kept the fraction 4/3 and I let the calculator handle the decimal digits of pi, so I could get the most accuracy possible.
Round that decimal value however needed.
It appears you forgot a zero in your result of .01021
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Part 2
n = number of spheres
0.0010226538586 = volume of 1 sphere
0.0010226538586n = volume of n spheres = amount of material
0.0010226538586n = 1
n = 1/0.0010226538586
n = 977.847970347451
n = 977
We can make about 977 spheres.
Your answer is off by a factor of 10 because you forgot a zero in your previous result.
Your previous result should be smaller by a factor of 10, making the second result larger by a factor of 10 (to counter-balance).
In cases like this, always round down to the nearest whole number. It doesn't matter that n = 977.84797 is closer to 978 compared to 977.
We do not have enough material to make the 978th sphere.
If you made 977 spheres, then you use up
0.0010226538586*977 = 0.9991328198522 cubic inches of material
But if you made 978 spheres, then you use up
0.0010226538586*978 = 1.0001554737108 cubic inches
Which is over the target of "1 cubic inch".
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