## 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.

1. jwuphysics

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

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

3. jwuphysics

Why not? The units make sense.

4. jwuphysics

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

5. rtraylor3

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