Suppose a 1 m³ cube of ice is transported without melting from Mount Everest to a location at sea level. The atmospheric pressures at the peak of Mount Everest and at sea level are 0.31 atm and 1 atm, respectively. Determine the change in the volume of ice (ΔV). Take the compressibility k of ice as 5.00 × 10^-10 Pa^-1.

A cylinder made of unknown material has a diameter of 8.0 cm and a height of 10 cm. An engineer wishes to house an axle at the center of the cylinder. Therefore, they drill a hole of diameter 4.0 cm at the center of the cylinder. The engineer measures the weight of the hollowed cylinder to be 25.0 N. Determine the density of the unknown material. 

A cylindrical object of diameter 20 cm and height 50 cm floats in oil (ρ = 915 kg/m³) with a length of 30 cm above the oil. Determine the object's density.

Equal volumes (V) of ethanol (ρ = 789 kg/m³) and cooking oil (ρ = 915 kg/m³) are accidentally mixed. Find the mean density of the mixture.

You wish to cast a spherical copper shell (hollow) with an inner diameter of 14 cm. You will do so using a 1.4 kg copper cube as the source material. Find the expected outer diameter of the shell. (Density of copper is 8900 kg/m³).

On the top of a hermetically sealed plexiglass cube with a side of 15.0 cm, a hair dryer blows air of density 1.06 kg/m³ at a speed of 50.0 m/s. Calculate the pressure difference ΔP between the inside and outside of the cube.