Dimensional analysis. Please check my working

[need_aca_help]

Homework Statement

Two spheres are cut from a certain uniform rock. One has radius 4.30 cm. The mass of the other is six times greater. Find its radius.

Homework Equations

v = (4/3)(pi)(r)^3
m = vp

The Attempt at a Solution

6[(4/3)(pi)(r₁)³] = (4/3)(pi)(r₂)³
8(pi)(r₁)3 = (4/3)(pi)(r₂)3
6(r₁)³ = (r₂)³
6(4.3)^(1/3) = 9.7568

Answer:
9.76 cm

I got this question wrong for some reason... Where is my mistake...?

 

[rude man]

6(r₁)³ = (r₂)³
6(4.3)^(1/3) = 9.7568

Answer:
9.76 cm

I got this question wrong for some reason... Where is my mistake...?

Going from 2nd last to last equation you made your basic mistake.

 

[need_aca_help]

I don't see it... :(

 

[SteamKing]

If you take a sphere with radius r, and make another sphere with radius 2*r, what is the ratio of the volume of the bigger sphere to the smaller sphere?

 

[rude man]

I don't see it... :(

Take the cube root of each side. Your mistake is on the left-hand side.
Fact: (ab³)^1/3 = a^1/3b