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

Question

anonymous · Answer

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:$${V_1 \over V_2} ={ {(2r_2)}^3 \over  {r_2}^3} = 2^3 = 8$$

anonymous · Answer

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

anonymous · Answer

Why not?  The units make sense.

anonymous · Answer

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

anonymous · Answer

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