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Sagot :
Answer:
To find the radius of the solid aluminum sphere that balances a solid iron sphere of radius 2.00 cm on an equal-arm balance, we need to calculate the mass of the iron sphere and then determine the radius of the aluminum sphere that has the same mass.
Given:
- Mass of iron sphere = 7.86 x 10³ kg
- Radius of iron sphere = 2.00 cm = 0.02 m
First, let's calculate the mass of the iron sphere using the formula for the volume of a sphere:
Volume of a sphere = (4/3) * π * r³
Where:
- r is the radius of the sphere
Mass of iron sphere = Density of iron * Volume of iron sphere
The density of iron is approximately 7.86 x 10³ kg/m³. Plugging in the values:
Mass of iron sphere = (7.86 x 10³ kg/m³) * ((4/3) * π * (0.02 m)³)
Mass of iron sphere = 7.86 x 10³ kg
Now, we need to find the radius of the aluminum sphere that has the same mass. The density of aluminum is approximately 2.70 x 10³ kg/m³. We can use the same formula to calculate the volume of the aluminum sphere:
Volume of aluminum sphere = (4/3) * π * r³
Mass of aluminum sphere = Density of aluminum * Volume of aluminum sphere
Now, we can set up an equation to find the radius of the aluminum sphere:
(7.86 x 10³ kg) = (2.70 x 10³ kg/m³) * ((4/3) * π * r³)
Solving for r³:
r³ = (7.86 x 10³ kg) / (2.70 x 10³ kg/m³)
r³ = 2.91 x 10⁰ m³
Taking the cube root of both sides to find the radius of the aluminum sphere:
r = (2.91 x 10⁰ m³)^(1/3)
r ≈ 1.70 m
Therefore, the radius of the solid aluminum sphere that balances a solid iron sphere of radius 2.00 cm on an equal-arm balance is approximately 1.70 m.
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