Answer :
Final answer:
To find the average density of the star, we divide its mass by its volume. The volume of a sphere is calculated using the formula V = (4/3)πr³. Converting the given radius from kilometers to centimeters allows us to calculate the volume. Using the density formula, we can then determine the average density of the star in grams per cubic centimeter.
Explanation:
To find the average density of the star, we need to divide its mass by its volume. The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. In this case, the average radius of the star is given as 6.2 ✕ 10⁵ km. We need to convert this to centimeters by multiplying it by 10⁵ to get 6.2 ✕ 10¹⁰ cm. Plugging the values into the formula, we have V = (4/3)π(6.2 ✕ 10¹⁰)³ cm³.
We can use the density formula, density = mass/volume, to calculate the average density of the star. Given that the mass is 2.0 ✕ 10³⁶ kg and the volume calculated previously, we can substitute the values into the formula as density = (2.0 ✕ 10³⁶ g) / [ (4/3)π(6.2 ✕ 10¹⁰)³ cm³ ].
Simplifying this expression will give us the average density of the star in units of grams per cubic centimeter.
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