The radius of one sphere is twice as great as the radius of a second sphere.

Find the ratio of their volumes.

Question

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

mven · Answer

@iGreen Help please!!

anonymous · Answer

What's the equation to calculate the volume of a sphere if you know the radius?

mven · Answer

4pir^2

mven · Answer

I got 8 but that was wrong

anonymous · Answer

Well, I guess if you use any arbitrary number for the radius, and calculate the volume, and then do the same for a radius twice as big, and then divide the volumes from each other, that would do the trick?

mven · Answer

got 1:2 ?

anonymous · Answer

8 is pretty close actually

mven · Answer

it said that it was wrong. I thaught 8 too. otherwise it gives me
 1/2
1/4
1/8
1/16

I dont think that 1/8 and 1/4 would work.

mven · Answer

it said 1/8 was wrong anyway

anonymous · Answer

Ah right, 1/8 as it's a ratio.

anonymous · Answer

So the one is 8 times bigger to the other, as a ratio you write 1/8 (as in, if the one has a volume of 1, the other has a volume of 8)

mven · Answer

ah, Makes sense. so one being 2 times larger as the other the ratio would be 1/2 ?

anonymous · Answer

True, but note that if the radius has a ratio of 1/2 the volume has a ratio of 1/8 because

$$\frac{ 4 }{ 3 }*\pi* r^3 = x*\frac{ 4 }{ 3 }*\pi*(2r)^3 $$

If you solve this either r=0 or x=1/8

anonymous · Answer

That is because the radius is to the power of 3 and 2^3 is 8

mven · Answer

ahh, Makes sense. Thanks for the help!!