BRAVO! That is the correct answer!

We will make the approximation that the ship's hull underwater is a rectangular solid with length of L = 280 m

and a width of

w = 30 m

and a "draft" or depth of h

That means the volume of water that is displaced is

V = L w h = (280 m) (30 m) h

V = (8400 m²) h

This volume of sea water has a mass of

M = V

M_water = (1025 kg/m³) (8400 m²) h

M_water = ( 8,610,00 kg/m ) h

M_water = ( 8.61 x 10 ⁶ kg/m ) h

There will be an m, for meters, in h. That is, h will be so many meters. That means that M_water will, indeed, be measured in units of kg, kilograms.

Be careful now. This is a mass. We know weight is a force and will be measured in units of Newtons. However, we are given that the Magic's displacement or weight is 77,000 metric tons. A metric ton is the weight of 1,000 kg (or 1,000 kg-wt). That is the weight of

77 x 10⁶ kg

or

W = (77 x 10⁶ kg) g

The bouyant force is

F_bouy = W_water

F_bouy = M_water g

Now set the bouyant force equal to the weight of the vessel,

F_bouy = M_water g = (77 x 10⁶ kg) g = W

M_water g = (77 x 10⁶ kg) g

M_water = (77 x 10⁶ kg)

This mass of the water is determined by the volume,

M_water = V

We have already evaluated this,

M_water = ( 8.61 x 10 ⁶ kg/m ) h

M_water = ( 8.61 x 10 ⁶ kg/m ) h = (77 x 10⁶ kg)

h = (77 x 10⁶ kg) / (8.61 x 10 ⁶ kg/m)

h = 8.9 m

Remember, we used some reasonable approximations. The actual "draft" or depth is about 7.7 m.

(c) 2000, Doug Davis; all rights reserved.