Question

The volumes of two spheres are in a ratio of 1:8 what is the eatio rafi

Answer 1

Remark
I take it that you want to know the ratio of the radii. If this is not correct, leave a comment below my answer.

You could do this by giving the spheres a definite volume, like 1 and 8 and then solve for r for one of them and then use the other sphere to find it's radius. It is not exactly the best way, and if you are going to to a physics class you want to be doing this using cancellation.

Step One
Set up the Ratio for the volumes.


`(V_1)/(V_2) = (1)/(8)`

Step Two
Setup the equation for V1/V2 using the definition for a sphere. V = 4/3 pi r^3


`(1)/(8) = ( (4)/(3) \pi( r_1)^3 )/( (4)/(3) \pi( r_2)^3 )`

Step Three
Cancel the 4/3 and pi on the top and bottom of the fractions on the right.

You are left with 1/8 = (r1)^3/ (r2)^3

Step Four
Take the cube root of both sides.
cube root 1/8 = 1/2

Cube root of (r1)^3 = r1
Cube root of (r2)^3 = r2

Step Five
Answer

`(r_1)/(r_2) = (1)/(2)` Answer <<<<<<<