IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng mga maaasahang sagot. Hanapin ang impormasyon na kailangan mo nang mabilis at madali sa pamamagitan ng aming komprehensibo at eksaktong platform ng tanong at sagot.
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.
Ang iyong aktibong pakikilahok ay mahalaga sa amin. Magpatuloy sa pagtatanong at pagbahagi ng iyong nalalaman. Sama-sama tayong lumikha ng isang masiglang komunidad ng pagkatuto. Para sa mga de-kalidad na sagot, piliin ang IDNStudy.com. Salamat at bumalik ka ulit sa aming site.
