What Would Be the Mass of an Iron-Dense Empire State Building?

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The mass of an iron-dense Empire State Building, with an estimated volume of 37 million cubic feet, can be calculated by converting the volume to cubic meters and multiplying it by the density of iron (7870 kg/m³). This results in a mass of approximately 8.18 billion kilograms. A follow-up question discusses the energy required to propel this mass at Mach 7 speeds, using the kinetic energy formula (1/2 mv²). The calculations assume 100% efficiency and no air resistance. This highlights the significant mass and energy considerations for such a hypothetical scenario.
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If an object the size of the empire statbuilding had iron density,what would be ...

the mass of it?

The estimated volume of the empire state building is 37 million cubic feet,how could I calculate the mass of this solid object if it had a density of Iron(which would be 7870 kg/m³)?
 
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Multiply the density by the volume.
 


So I converted the ft^3 to m^3 and I have 1.04 million m^3* 7870kg/m^3=8184800000 kg/m^3.Did I do this right or do I have to remove the kg/m^3?
 


Wow if I am correct is that over 8 billion kilograms of mass?
 


So here is a follow up question,how much energy would be required to propel this object at Mach 7 speeds?
 


1/2 mv2

m=mass in kg
v=speed in meters / second

That would be if the propulsion device was 100% efficient and there was no air resistance.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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