# Dimensional analysis. Please check my working

## 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

9.76 cm

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

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rude man
Homework Helper
Gold Member

6(r1)3 = (r2)3
6(4.3)(1/3) = 9.7568

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.

I don't see it... :(

SteamKing
Staff Emeritus
Homework Helper
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
Homework Helper
Gold Member
I don't see it... :(
Take the cube root of each side. Your mistake is on the left-hand side.
Fact: (ab3)1/3 = a1/3b