What is the Tension in the String Holding a Submerged Cork?

[DLH112]

Homework Statement

A cork is held at the bottom of a bucket of
water by a piece of string. The actual depth
of the cork is 0.713786 m below the surface of
the water.

If the density of the cork is 157 kg/m3
and the volume of the cork is 3 cm3
, then what is the tension in the string? The acceleration
of gravity is 9.8 m/s
2
. Assume the density of
water is 1000 kg/m3
.

Homework Equations

d= m/v Fb= weight of displaced fluid

The Attempt at a Solution

The tension should be the force required to keep it in equilibrium...
using d=m/v, into dv = m (1000)(0.03) = 30 kg (mass of displaced water)(9.8)
weight of displaced water = Fb = 294 N
using dv = m again for the cork. (157)(0.03) = 4.71 kg (9.8) = 46.158 N

294 - 46.158 = 247.842 N .
Its a multiple choice answer and the choices are either that number but the decimals in the wrong place (all the answers are smaller), or 0.0123921 N.
maybe I'm supposed to use the depth and P=pgh somehow if that other numbers right, but I'm not sure how it would apply to this problem.

 

[SteamKing]

Units, Units, Units!

3 cm^3 is not the same as 0.03 m^3

You are essentially saying that 3 cc of water has a mass of 30 kg!

 

[DLH112]

that makes sense... so it would be like (0.03)^3 then i guess

 

[haruspex]

Looks like the problem setter didn't think of this particular mistake, or there would have been a choice to match.