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

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jwuphysicsBest ResponseYou've already chosen the best response.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:\[{V_1 \over V_2} ={ {(2r_2)}^3 \over {r_2}^3} = 2^3 = 8\]
 one year ago

rtraylor3Best ResponseYou've already chosen the best response.0
The ratio is 8? That doesn't make sense.
 one year ago

jwuphysicsBest ResponseYou've already chosen the best response.2
Why not? The units make sense.
 one year ago

jwuphysicsBest ResponseYou've already chosen the best response.2
This basically means that the first sphere is 8 times as large as the second sphere.
 one year ago

rtraylor3Best ResponseYou've already chosen the best response.0
Oh!! That's what I didn't get! Thanks!
 one year ago
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