Standards of Length, Mass, and Time

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Homework Help Overview

The problem involves determining the radius of a sphere based on its mass relative to another sphere made from the same uniform rock. The context includes concepts of volume, density, and the geometric relationship between the radius and volume of a sphere.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between mass, volume, and density, and how these relate to the radius of a sphere. There is an exploration of the relevant equations and their application to the problem.

Discussion Status

The discussion has progressed with participants providing guidance on the relationships between the physical properties involved. A participant has successfully derived a solution based on the established relationships.

Contextual Notes

Assumptions about uniform density and the geometric properties of spheres are central to the discussion. The original poster expressed uncertainty about the initial approach to the problem.

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


Not sure what equations to use for it

I am not sure how to attempt this problem?
 
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Mass is volume times density. 'Uniform' rock means you can assume the two rocks have the same uniform density. Now do you know a relation between the radius of a sphere and the volume?
 
Volume equals (4/3)pi radius^3
 
Good then you are all set to go. Try solving it.
 
Thanks I got it. So I set the two relations equal to each other m1/v1=m2/v2. Substitute volume for their equation of (4/3)pi radius^3 and solve for r2.
 
The answer I got was 5.4 cm, which is right thanks again.
 

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