Answer :
If a Styrofoam has a density of 300 kg / m³, the maximum mass that can hang without sinking from a 20.0 cm -diameter Styrofoam sphere in water is 23.45 kg
ρ = m / V
V = 4 / 3 π r³
ρ = Density
m = Mass
V = Volume
r = Radius of sphere
d = 40 cm = 0.4 m
r = d / 2 = 0.4 / 2
r = 0.2 m
V = 4 / 3 * 3.14 * 0.2 * 0.2 * 0.2
V = 0.0335 m³
ρ = 300 kg / m³
m = ρ V
m = 300 * 0.0335
m = 10.05 kg
Similarly for water displaced,
ρ = 1000 kg / m³
m = 1000 * 0.0335
m = 33.5 kg
The maximum mass that the sphere can hold without sinking,
m = 33.5 - 10.05
m = 23.45 kg
Therefore, the maximum mass that the sphere can hold without sinking is 23.45 kg
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