Calculate Radius of Equal Mass Aluminum and Gold Spheres | Formula Included

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Homework Help Overview

The problem involves calculating the radius of an aluminum sphere that has the same mass as a gold sphere of a specified radius. The context includes the densities of aluminum and gold, with a focus on significant figures in the final answer.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the significance of using the correct number of significant figures in their answers. There is mention of using density and volume relationships to set up equations for the spheres based on their radii.

Discussion Status

Some participants have provided guidance on significant figures and the relationship between mass, density, and volume. Others express confusion about the complexity of the problem and are exploring different methods to simplify their approach.

Contextual Notes

There is a focus on ensuring the answer adheres to significant figure rules, and participants are questioning whether the initial assumptions and calculations are correct. The original poster expresses frustration with the problem's complexity.

mh922253
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hi again
i need help with this question!
One cubic meter (1.00 m3) of aluminum has a mass of 2.70×103 kg, and 1.00 m3 of gold has a mass of 1.93×104 kg. Find the radius of a aluminum sphere whose mass is the same as that of a gold sphere of radius 1.70 cm.


i tried it over 15 times every time i enter an answer, it says "Please adjust significant figures, you provided 2 significant figures"
my answer was 0.017m
what do u think...pleasezzzz help me
 
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0.017m is 2 sf. Try 3 sf, 0.0170m.
 
All of the information was given with 3 significant figures and its all multipliction and division to get the answer, so you should give the answer to 3 sig figs. That would make your answer .0170m instead of .017m, but I don't believe that is the correct answer. Remember that the mass is the density times the volume. So the volume of the gold sphere times the density of gold equals the volume of the aluminum sphere times the density of aluminum. Put the equations in for the volume of the spheres in terms of their radii, and solve for the unknown radius of the aluminim sphere.
 
it is still the wrong answer I am going to try leonhardeuler's way thanks anyways
it is so complicated i donno how to make it simpler
 

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