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rtraylor3

  • 2 years ago

The radius of one sphere is twice as great as the radius of a second sphere. Find the ratio of their volumes.

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  1. jwuphysics
    • 2 years ago
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    Volume of a sphere:\[V= {4\over3}\pi r^3\] Let's call your two radii r_1 and r_2, where\[r_1 = 2 r_2\]Then we can quickly see:\[V_1 = {4\over3} \pi {r_1}^3\] and \[V_2 = {4\over3} \pi {r_2}^3\]Substituting in the fact that r_1 is double r_2, we find\[V_1 = {4\over3} \pi {(2r_2)}^3\]The ratio of volumes, if you cancel out the 4/3 and pi's, is:\[{V_1 \over V_2} ={ {(2r_2)}^3 \over {r_2}^3} = 2^3 = 8\]

  2. rtraylor3
    • 2 years ago
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    The ratio is 8? That doesn't make sense.

  3. jwuphysics
    • 2 years ago
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    Why not? The units make sense.

  4. jwuphysics
    • 2 years ago
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    This basically means that the first sphere is 8 times as large as the second sphere.

  5. rtraylor3
    • 2 years ago
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    Oh!! That's what I didn't get! Thanks!

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