How Do You Determine the Radius of a Sphere If Its Mass is Seven Times Another?

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Homework Help Overview

The problem involves determining the radius of a sphere based on its mass relative to another sphere. The context is within the subject area of physics, specifically dealing with concepts of density and volume of spheres.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between mass and volume, referencing the formulas for density and volume of a sphere. There is an exploration of the ratio of radii based on mass ratios, and one participant shares a calculated volume for the first sphere.

Discussion Status

The discussion includes attempts to apply relevant formulas and explore relationships between the spheres. While one participant claims to have found an answer, the process leading to that conclusion is not fully detailed, leaving room for further exploration of the reasoning involved.

Contextual Notes

Participants are working with the assumption that the spheres are made from the same material, which implies uniform density. There is also mention of a specific mass relationship between the two spheres, which is central to the problem.

ramin86
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I'm really bad at physics and need help with the following question:

Two spheres are cut from a certain uniform rock. One has radius 4.95 cm. The mass of the other is seven times greater. Find its radius.
 
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The average density of an object is:

[tex]\rho = \frac{m}{V}[/tex]

Where m is mass and V is volume

The volume of a sphere is:

[tex]V = \frac{4\pi}{3} r^3[/tex]

Where r is the radius.

These are the only two formulas you need.
 
Does this look familiar?

[tex]\frac {R_1}{R_2} = \left(\frac{M_1}{M_2}\right)^{\frac{1}{3}[/tex]
 
Alright, well I got a volume of 508.05 for the sphere with a radius of 4.95, but still not exactly sure of where to go from here.
 
Okay, nevermind, I got the answer at 9.469
 

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