SOLUTION: Does someone know how to go about solving this? A spherical container has a volume. If another has twice the volume of the first, how do the radiis compare? Explain your answer

Algebra ->  Volume -> SOLUTION: Does someone know how to go about solving this? A spherical container has a volume. If another has twice the volume of the first, how do the radiis compare? Explain your answer      Log On


   

Question 708604: Does someone know how to go about solving this?
A spherical container has a volume. If another has twice the volume of the first, how do the radiis compare? Explain your answer briefly.
HHHEELLPP!!
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The two spheres each have their own radius. The large sphere may have r[b] and the small sphere may have radius r[s]. b for big, s for small.
v=%284%2F3%29%2Api%2Ar%5E3 for a sphere, volume.

You can treat your description like small sphere, v; large sphere, 2v.
You have
v=%284%2F3%29%2Api%2Ar%5Bs%5D%5E3 and 2v=%284%2F3%29%2Api%2Ar%5Bb%5D%5E3

Your goal was to compare the radius of the big sphere to the radius of the sphere of half the volume. You could solve each of the above volume equations for r[s] and r[b], and then compare them.

r%5Bs%5D=root%283%2C%28%283%2F%284%2Api%29%29v%29%29 and r%5Bb%5D=root%283%2C%28%283%2F%284%2Api%29%292v%29%29

You should factor those, like this:
r%5Bs%5D=root%283%2C3%2F%284%2Api%29%29%2Aroot%283%2Cv%29 and r%5Bb%5D=root%283%2C3%2F%284%2Api%29%29%2Aroot%283%2C2v%29.
even further,
r%5Bs%5D=root%283%2C3%2F%284%2Api%29%29%2Aroot%283%2Cv%29 and r%5Bb%5D=root%283%2C3%2F%284%2Api%29%29%2Aroot%283%2Cv%29%2Aroot%283%2C2%29.

When you look at the ratio of r%5Bb%5D to r%5Bs%5D, you will eliminate the root with the constants. (cancelling as k/k=1).

To finally finish this, write the ratio of r%5Bb%5D to r%5Bs%5D.
%28r%5Bb%5D%2Fr%5Bs%5D%29=?what?