Question

Steel has a density of 8.0 g/cm3. Let's plan building a spherical shell, made out of 2.0 cm thick steel. The perfectly spherical shell will have outer diameter of 2.0m. You can think of such a shell as a solid sphere, and then you cut out a sphere that has a 2.0cm smaller radius. 2. How heavy is that hollow sphere? Would this sphere float in water? a. b.

Answer 1

density of steel= 8.0 g/cm^3 = 8000Kg/m^3

outer dia = 2.0m thickness of shell = 2 x 10^(-2) mrs

volume of steel = (4/3) (pi) {R^3-r^3} where R = 2.0 mts and r = 1.98 mts

= (4/3) (pi) ( 2^3 - 1.98^3) = 0.995 m^3

mass of hollow sphere = Volume x density = 8000 Kg/m^3 x 0.995 m^3 = 7960 Kg

b.

density of water = 997 kg/m^3

density of Steel shell = Mass of shell /Volume of sphere = 7960 Kg / (4/3) (pi) 2^3 = 237.5 Kg/m^3

density of water > density of steel shell =====> Steel shell will float on the water