Fluid Mechanics problem?

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I have a question related to fluid mechanics. A lead sphere and an aluminum sphere have the same mass and are uniform in structure. What is the ratio of the radius of the aluminum sphere to that of the lead sphere? Given that the density of lead is ( 11.3 	imes 10^3 \, 	ext{kg/m}^3 ) and the density of aluminum is ( 2.7 	imes 10^3 \, 	ext{kg/m}^3 ), I would appreciate guidance on how to set up this problem. Thank you for any help!

Peyton Kiehn · Accepted Answer

You just need to know the formula for the volume of a sphere (vol = 4/3pir^3, where r is the radius) and the relationship between density, mass, and volume ( mass = density * volume ). 
Then 
Pb_density / Al_density = (Pb_mass/Pb_volume) / (Al_mass/Al_volume) = (mass/Pb_volume)/(mass/Al_volume)  -- this last because the masses are the same.
So
Al_volume/Pb_volume = Pb_density/Al_density ~ 4.19.
Thus,
(4/3piAl_radius^3) / (4/3piPb_radius^3) ~ 4.19     (and this makes sense, because you'd expect the Al sphere to be a bit larger than the lead sphere if they have the same mass). 
So (Al_radius / Pb_radius) ^3 ~ 4.19
==> Al_radius/Pb_radius ~ (4.19)^(1/3) ~ 1.6.
  The Al sphere will be 1.6 times the radius of the Pb sphere.

Candelario Christiansen · Answer

A uniform lead sphere and a uniform aluminium sphere have the same mass what is the ratio of the radius of aluminium sphere to the radius of the lead sphere?

Theodore Schmeler · Answer

a uniform lead sphere and a uniform aluminum sphere have the same mass. what is the ratio of their radius

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Fluid Mechanics problem?

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