The following questions involve using Archimedes' Principle:

1) Spherical particles have a density of 1.30 x 10^3 kg m^-3 and a radius of 0.22 x 10^-6 m.

a) What is their mass?

b) What is their apparent weight in water?

The correct answers are: a) 5.8 x 10^-17 kg b) 1.3 x 10^-16 N. Please provide a detailed explanation of how to achieve these answers.

2) An ice cube of density 917 kg m^-3 floats in a martini of density 925 kg m^-3. What fraction of the ice cube is submerged?

The correct answer is: 0.991, please provide a detailed explanation of how to achieve this answer.