Fluids (Find the tension)

[Bcisewski]

I could use some help on what formula or combination of formulas I am missing.
An iron (p = 7860 kg/m3) cube measuring 15.4 cm on a side is suspended from a wire. Find the tension in the wire when the block is completely submerged in water (p = 1000 kg/m3). The answer is 246 N

1) I have tried first to find the volume, v=m/p or v*p=m 3652*7860=28706795.04 , (3652=v, 15.4 cubed)
2) I tried then to find F of the block with, Fb=(3562)(1000)(9.81)=35789600
3) I then used both numbers in a final eq. FT=mg-Fb (28706795)(9.81)-(35789600)= to big of number

Thanks for the help.

[Astronuc]

Note that the density is given in kg/m^3, but the side length is given in cm. So be careful not to mix units.

The volume of a cube 15.4 cm on a side is of course 15.4^3 or 3652.264 cm^3. 1 m = 100 cm, so the volume, V, = 0.0036523 m^3.

The tension,T, in the wire, which is simply the gravitational force exerted on the block, is given by,

T = (m(block) - m(water))g.

m\,=\,\rho\,V

Note that the block is completely submerged so it displaces an equal volume of water.