Buoyancy: Cube of Iron - solved this correctly?

[snowcrystal42]

Hi,
Just wondering if I'm going about solving this problem correctly:

"A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 1.6 m on each side is made into sheets. From these sheets, to make a hollow cube that will not sink, what should the minimum length of the sides be? (density of iron = 7860 kg/m³)"

Since it's a solid cube of iron, the volume of iron = 1.6³ = 4.096 m³

Mass of iron = density of iron x volume

Since the hollow cube is floating, it is under forces mg (weight of the iron) and the buoyant force, which are equal to each other.

mg_(iron) = ρ_(water) x V_(water) x g
g drops out of equation
so V_(water) = mg_(iron)/ρ_(water)

V_(water) = 32.19 m³

Since the shape is supposed to be a hollow cube, each side length is the cube root of the volume, so each side is (32.19)^⅓ = 3.18 m

Thanks!

 

[J Hann]

That appears correct.