Answer:
1.257 kilograms is the maximum mass that can hang without sinking.
Explanation:
Mass of styrofoam = m
Volume of the sphere = V
V = [tex]\frac{4}{3}\pir^3[/tex]
Diameter of the sphere = d = 20.0 cm
Radius of the of sphere = r = 0.5 d = 10.0 cm = 0.1 m ( 1 cm = 0.01 m)
[tex]V=\frac{4}{3}\times 3.14\times (0.1 m)^3=0.00419 m^3[/tex]
Density of the sphere = [tex]\rho =300 kg/m^3[/tex]
[tex]Density=\frac{Mass}{Volume }[/tex]
Weight of the styrofoam sphere , [tex]W= \rho Vg[/tex]
[tex]m \times g=\rho Vg[/tex]
[tex]m=\rho V[/tex]
[tex]m=\rho \times V = 300 kg/m^3\times 0.00419 m^3=1.257 kg[/tex]
1.257 kilograms is the maximum mass that can hang without sinking.
The maximum mass that can hang without sinking from a 20.0 cm -diameter Styrofoam sphere in water is 1.256kg
The formula for calculating the density of an object is expressed as:
[tex]Density=\frac{Mass}{Volume}[/tex]
Given the following parameter
Density = 300kg/m³
Volume of the sphere = [tex]\frac{4}{3} \pi r^3[/tex]
r is the radius = 10/2 = 10cm = 0.1m
Get the volume of the Styrofoam sphere
[tex]V_s=\frac{4}{3} \times 3.14\times(0.1)^3\\V_s= 0.004187 cm^3[/tex]
Get the required mass:
[tex]Mass = density \times volume\\Mass = 300 \times 0.004186\\Mass=1.256kg[/tex]
Hence the maximum mass that can hang without sinking from a 20.0 cm -diameter Styrofoam sphere in water is 1.256kg
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