The mass of the float is 50.0 kh and it has a volume of 1.0 m^3.det ermine the density of the float and the tension on the rope. You may assume g=10N/kg.

So I know that
mfloat = 50.0kg
weight of float = 50.0 x 10 = 500N
Vfloat = 1.0 m^3
density of Sea water = 1000kg/m^3

D=m/v...50.00kg/1.0m^3 = 50kg/m^3.

then for the tension of the rope I need to calculate the Buoyant force via Archemde's principle ...I get lost right around here can anyone make corrections and show me how it's done?

You didn't give all of the INFO.

Density = m/V = 50kg/1m^3 = 50kg/m^3