- #1

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The radii of four different-sized ball bearings differ by 1.0mm in radius from one size to the next. If the volume of the largest equals of the other three combined, find the radii.

Any help is greatly appreciated!

- Thread starter notsosmartman
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- #1

- 6

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The radii of four different-sized ball bearings differ by 1.0mm in radius from one size to the next. If the volume of the largest equals of the other three combined, find the radii.

Any help is greatly appreciated!

- #2

- 218

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Now we know that the radii differ by 1mm for each successive sphere, and we also know that the volume of the smaller three sum up to the larger sphere.

Therefore we know that

[tex]\frac{4}{3}\pi((x-1)^{3} + (x-2)^{3} + (x-3)^{3}) = \frac{4}{3}\pi x^{3}[/tex]

which we can simplify into

[tex]x^{3} - 9x^{2} + 21x - 18 = 0[/tex]

now there are numerous ways to solve this equation which I will not go into.

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