1.) 0.68 g/cm^3
2.) 4.3 × 10^16 m^2
Explanation:
Given that the radius of the planet Saturn is 5.85 ✕ 107 m, and its mass is 5.68 ✕ 1026 kg.
Where (The volume of a sphere is given by 4/3 πr3.)
Substitutes r into the parameters
V = 4/3π × ( 5.85 × 10^7)^3
V
≈ 4/3 × 3.14159 × (5.85 × 10^7)^3
≈ 4/3 × 3.14159 × 1.03014 × 10^23
≈ 4.0844 × 3.14159 × 1.03014 × 10^23
≈ 12.826 × 1.03014 × 10^23
≈ 13.205 × 10^23
≈ 1.32 × 10^24 m^3
Now, we can calculate the density using the formula:
Density = Mass/Volume
Density = 5.68 × 10^26 kg / 1.32 × 10^24 m^3
≈ 4.30303 × 10^(26-24) kg/m^3
≈ 4.30303 × 10^2 kg/m^3
≈ 430.303 kg/m^3
Converting kg/m^3 to g/cm^3:
Density = 430.303 kg/m^3 × (1 g/1000 kg) × (100 cm/1 m)^3
≈ 4.30303 g/cm^3
So, the average density of Saturn is approximately 4.303 g/cm^3.
Therefore, option 1 is correct: 0.68 g/cm^3 is incorrect.
As for option 2: 4.3 × 10^16 m^2, it is not related to the density calculation and appears to be unrelated and not applicable in this context, so it is also incorrect.
= 4/3 × 3.14 × (5.85 × 10^7)^3
= 4/3 × 3.14 × (5.85 × 10^7)^3
= 4/3 × 3.14 × (5.85^3) × (10^7)^3
= 4/3 × 3.14 × 197.155 × 10^21
= 261.90 × 10^21 m^3
Now we can calculate the density using the formula:
Density = Mass / Volume
Density = 5.68 × 10^26 kg / 261.90 × 10^21 m^3
= (5.68 / 261.90) × (10^26 / 10^21)
= 0.0217 × 10^5 kg/m^3
= 2.17 × 10^3 kg/m^3
Therefore, the density of Saturn is approximately 2.17 × 10^3 kg/m^3.