Dimensional analysis. Please check my working

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Homework Help Overview

The problem involves two spheres made from a uniform rock, where one sphere has a radius of 4.30 cm and the other has a mass six times greater. The objective is to find the radius of the second sphere using dimensional analysis and volume equations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the volumes of the spheres based on their radii and mass. There is an attempt to equate the volumes derived from the radii and to identify mistakes in the calculations.

Discussion Status

Participants are actively questioning the calculations made by the original poster, particularly focusing on the transition between equations. Some guidance has been provided regarding the mathematical manipulation of the equations, but no consensus on the exact mistake has been reached.

Contextual Notes

There is an indication that the original poster may have misapplied the cube root in their calculations, but the specifics of the error are still under discussion.

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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...?
 
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need_aca_help said:


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.
 
I don't see it... :(
 
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?
 
need_aca_help said:
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
 

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