Assume that the mass of a sun-like star is 2.50 x 10^5 Earth masses and that its radius is about 101.0 times that of Earth. The density of Earth is about 5,500 kg/m^3. What is the density of this star?
To find the density of the star, we need to divide its mass by its volume.
First, let's calculate the volume of the star. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
Given that the radius of the star is about 101.0 times that of Earth, we can calculate the radius of the star as 101.0 * radius of Earth.
Next, let's calculate the volume of the star using the formula mentioned earlier.
V = (4/3) * π * (101.0 * radius of Earth)³
Now that we have the volume of the star, we can calculate its density by dividing its mass by its volume.
Density = mass of the star / volume of the star
Density of star = (2.50 x 10^5 Earth masses * mass of Earth) / [(4/3) * π * (101.0 * radius of Earth)³]
To calculate the final answer, substitute the values for the mass and radius of the Earth:
mass of Earth = 5.972 × 10^24 kg
radius of Earth = 6,371 km = 6,371,000 m
Now we can plug the values into the equation and calculate the density of the star.