We are given that the density of water is:
density (d) = 1 x 10^-3 kg / cm^3
Therefore
A. given volume = 1 m^3 , we need to find the mass but before that let us convert the volume into units of cm^3:
volume = 1 m^3 * (100 cm / 1 m)^3 = 1,000,000 cm^3
So the mass is simply density times volume:
mass = (1 x 10^-3 kg / cm^3) * 1,000,000 cm^3
mass = 1,000 kg
B. We are given that the diameter of the sphere is:
diameter = 1.0 µm or 1 x 10^-4 cm
The volume of a sphere can be calculated as:
V = (4/3) π r^3
V = (4/3) π (1 x 10^-4 cm / 2)^3
V = 5.236 x 10^-13 cm^3
So the mass is:
mass = (1 x 10^-3 kg / cm^3) * 5.236 x 10^-13 cm^3
mass = 5.236 x 10^-16 kg = 5.236 x 10^-13 g
C. We are given the radius = 4 cm
The volume of a sphere can be calculated as:
V = (4/3) π r^3
V = (4/3) π (4 cm)^3
V = 268.08 cm^3
So the mass is:
mass = (1 x 10^-3 kg / cm^3) * 268.08 cm^3
mass = 0.268 kg = 268 g
D. We are given the dimensions of the cylinder:
height = 4 mm = 0.4 cm
diameter = 2 mm = 0.2 cm
The volume of a cylinder is calculated as:
V = π r^2 h
V = π (0.2 cm/2)^2 * 0.4 cm
V = 0.0126 cm^3
So the mass is:
mass = (1 x 10^-3 kg / cm^3) * 0.0126 cm^3
mass = 1.26 x 10^-5 kg
