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

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To find the radius of an aluminum sphere with the same mass as a gold sphere of radius 1.70 cm, the mass of each sphere must be calculated using their respective densities. The mass of the gold sphere is determined by its volume and density, which is then equated to the mass of the aluminum sphere. The discussion highlights the importance of significant figures, suggesting that the answer should be presented with three significant figures, resulting in 0.0170 m. However, the user expresses frustration with the complexity of the calculations and is seeking alternative methods to simplify the process. The conversation emphasizes the need for clarity in applying formulas related to volume and density in solving the problem.
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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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