Dimensional analysis. Please check my working

AI Thread Summary
The discussion revolves around a homework problem involving the calculation of the radius of a sphere given its mass relative to another sphere. The initial equations used for volume and mass are correct, but the mistake occurs in the manipulation of the equations. Specifically, the error arises when transitioning from the equation involving the cube of the radii to the final calculation. The correct approach requires taking the cube root of both sides to find the radius of the larger sphere. Ultimately, the correct radius is not 9.76 cm, indicating a miscalculation in the process.
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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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