Standards of Length, Mass, and Time

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To find the radius of the second sphere, the relationship between mass, volume, and density is crucial, given that both spheres are made of the same uniform rock. The volume of a sphere is calculated using the formula (4/3)πr^3. By setting the mass-to-volume ratio equal for both spheres, the equation m1/v1 = m2/v2 can be used. Substituting the volume formula into this equation allows for solving the radius of the second sphere, which is found to be 5.4 cm. This approach effectively demonstrates the application of geometric and physical principles to solve the problem.
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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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