Question

Two spheres have a volume ratio of 27:8. What is the ratio of their radii?

Answer 1

I don't get how to do this.

Answer 2

@JoannaBlackwelder

Answer 3

I think that the radii would be the ratio of the cube roots of the volumes.

Answer 4

Let say the volume of big sphere is V1
and the volume of small one is V2,
and we have \(\dfrac{V1}{V2}=\dfrac{27}{8}\)
ok so far? not finish yet, but I need know you got it or not.

Answer 5

@claritamontano I am waiting for your reply to step up.

Answer 6

Yeah I get it,

Answer 7

We have formula to find the volume of the sphere. It says
V= \(\dfrac{4}{3}\pi r^3\) where r is radius of the sphere,
so that, we have \(V1= \dfrac{4}{3}\pi r_1^3\)
and \(V2= \dfrac{4}{3}\pi r_2^3\)
so far so good?

Answer 8

Yeah.

Answer 9

so, just plug in V1/V2 = 27/8
you have \(\dfrac {r_1^3}{r_2^2}=\dfrac{27}{8}\)
or \(\dfrac{r_1}{r_2}= \dfrac{3}{2}\)

Answer 10

ah I get it so my answer would now be 3:2

Answer 11

got it? just algebra
\(\dfrac {r_1^3}{r_2^2}=(\dfrac{r_1}{r_2})^3=\dfrac{27}{8}=(\dfrac{3}{2})^3\)
which gives us the ratio of the radii is 3/2

Answer 12

yeah! thanks wait not 3:2 or is that the same thing?

Answer 13

the same 3:2

Answer 14

okay thanks I get it!