Respuesta :
The density of the ball is the percentage of the density of water
equivalent to the percentage of the volume immersed in water
Correct response:
- The density of the ball is 249.25 kg/m³
Methods used for calculating the density
Given:
A ball floating on water
Percentage of the ball immersed in water = 25% = 0.25
Required:
The density of the ball
Solution:
According to Archimedes' principle, we have;
The weight of the ball = Weight of the water displaced
Therefore;
Mass of the ball = Mass of the water displaced
Volume of water displaced = 25% of the volume of the ball
Let r represent the radius of the ball, we have;
[tex]Volume \ of \ water \ displaced = 0.25 \times \dfrac{4}{3} \cdot \pi \cdot r^3 = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^3}[/tex]
Mass of the ball = Mass of water displaced
Density of water = 997 kg/m³
Which gives;
[tex]Mass \ of \ ball\ W = \mathbf{ 997 \times \dfrac{1}{3} \cdot \pi \cdot r^3}[/tex]
[tex]Density = \mathbf{\dfrac{Mass}{Volume}}[/tex]
Therefore;
[tex]Density = \dfrac{997 \times \dfrac{1}{3} \cdot \pi\cdot r^3 }{\dfrac{4}{3} \cdot \pi \cdot r^3} = \dfrac{997}{4} = \mathbf{249.25}[/tex]
- The density of the ball, ρ = 249.25 kg/m³
Learn more about Archimedes' principle here:
https://brainly.com/question/775316
