Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

rtraylor3

  • 3 years ago

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

  • This Question is Closed
  1. jwuphysics
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The ratio is 8? That doesn't make sense.

  3. jwuphysics
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Why not? The units make sense.

  4. jwuphysics
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    This basically means that the first sphere is 8 times as large as the second sphere.

  5. rtraylor3
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh!! That's what I didn't get! Thanks!

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy