Question

What is the maximum mass that can hang without sinking from a 50-cm diameter Styrofoam sphere in water

Answer 1

This question is incomplete, the complete question is;

Styrofoam has a density of 32kg/m³.

What is the maximum mass that can hang without sinking from a 50-cm diameter Styrofoam sphere in water

Answer: the required maximum mass is 63.3459 kg

Explanation:

Given that;

diameter d = 50 cm = 0.5 m

radius r = 0.5 / 2 = 0.25 m

Styrofoam density = 32kg/m³

Volume of sphere V = 4/3 πr³.

we substitute

V = 4/3 π(0.25)³

V = 0.06544 m³

Mass of sphere M = Volume × Density

we substitute

Mass of sphere M = 0.06544 m³ × 32kg/m³

Mass of Sphere M = 2.09408 kg

Mass of the water it displace will be;

volume × density

we know that density of water = 1000 kg/m³

so

Mass of the water it displace = 0.06544 m³ × 1000kg/m³

= 65.44 kg

Now the difference between mass of water and mass of the Styrofoam will be the amount of mass that the sphere can support

so

65.44 kg - 2.09408 kg = 63.3459 kg

Therefore, the required maximum mass is 63.3459 kg