Respuesta :
Answer:
the maximum mass that can hang without sinking is 2.93 kg
Explanation:
Given: details:
sphere diameter d = 20 cm
so, radius r = 10 cm = 0.10 m
density of the Styrofoam sphere D = 300 kg/m3
sphere volume [tex]V = \frac{4}{3} \pi r^3[/tex]
[tex]=\frac{4}{3} \pi 0.10^3[/tex]
=4.18*10^{-3} m^3
we know that
[tex]Density = \frac{Mass}{Volume}[/tex]
mass M = Density * Volume
= (300)(4.18*10^{-3} m3)
=1.25 kg
mass of the water displace = volume *density of water
= 4.18*10^{-3} m3 * 1000
= 4.18 kg
The difference between the mass of water and mass of styrofoam is the amount of mass that the sphere can support
=4.18 kg -1.25 kg
= 2.93 kg
The maximum mass that the sphere can hold without sinking is 2.92 kg
To solve this problem, we need to understand the formula used in calculating the volume of a sphere and relate it to the density-mass ratio.
What is the volume of a sphere?
The volume of a sphere refers to the amount of space occupied in the sphere. It can be determined by using the formula:
The volume of a sphere [tex]\mathbf{=\dfrac{4}{3}\pi r^3 }[/tex]
where;
- the radius of the Styrofoam = 20/2 cm = 10 cm = 0.10m
The volume of a sphere [tex]\mathbf{=\dfrac{4}{3}\pi (0.10)^3 }[/tex]
The volume of a sphere = 0.0042 m³
Using the density, mass, and volume relation;
[tex]\mathbf{density = \dfrac{mass}{volume}}[/tex]
Mass = density × volume
where;
- the density of a Styrofoam sphere = 300 kg
Mass = 300 kg × 0.0042 m³
Mass = 1.26 kg
Similarly, the mass of the water displaced is = 4.18 kg
Therefore, the maximum mass that the sphere can hold without sinking is:
= 4.18 kg - 1.26 kg
= 2.92 kg
Learn more about the volume of a sphere:
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