Styrofoam has a density of 300 kg/m3. What is the maximum mass that can hang without sinking from a 98 cm diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere.
3 Answers

Radius of sphere: 49cm = 0.49m
Volume of sphere = 4/3* 3.14*0.49³
Volume = 0.493m³
To sink the sphere completely, the sphere would have to displace 0.493m³ = 493 litres = 493kg of water, which would mean that the sphere would have a total mass of 493kg.
Mass of sphere = 0.493*300 = 147.9kg
Additional mass required to sink sphere = 493147.9 = 345.1kg
Maximum mass, just as the sphere sinks = 345.1kg.

Styrofoam Sphere

The mass of the Styrofoam ball = Vd = 0.3 kg. The weight of the ball = 2.94 N The buoyancy force on the ball = 9.8 N The weight that can be supported by the ball is 9.8 N – 2.94 N = 6.86 N The maximum mass = 0.7 kg = 700 g