Buoyancy of Spheres: max mass added without sinking

[BennyQuixote]

Homework Statement

Styrofoam has a density of 300 kg/m³. What is the maximum mass that can hang without sinking from a 40-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere.

Homework Equations

F_B=p_oV_og
Volume of sphere: 4/3 π r³
p=m/V

The Attempt at a Solution

I tried this:
m_o/3.35 m³=300 kg/m³
Therefore,
m_o=1005 kg

So,
To find the exact amount of mass added to the Styrofoam sphere to sink in water:
1005k + m₂/3.35 m³=1000 kg/m³

Therefore:
m₂=2345 kg

This is obviously an obscenely large mass to make Styrofoam sink in water. Any help is appreciated.


Quixote

 

[rl.bhat]

Check the volume of the sphere.