Question

A star is estimated to have a mass of 3x10^36 kg. Assuming it to be a sphere with an average radius of 7.6x10^5 km, calculate the average density of the star in units of grams per cubic centimeter.

Answer 1

Given:
m = 3 x 10³⁶ kg, the mass of the star
r = 7.6 x 10⁵ km = 7.6 x 10⁸ m

Calculate the volume of the star (as the volume of a sold sphere).

`V= (4 \pi )/(3) (7.6 * 10^(8) \, m)^(3) = 1.8388 * 10^(27) \, m^(3)`

Calculate the density the star.
By definition, the density of the star is

`\rho = (m)/(V) = (3 * 10^(36) \, kg)/(1.8388 * \, m^(3))=1.6315 * 10^(9) \, (kg)/(m^(3))`

In g/cm³, the density is

`(1.6315 * 10^(9) \, (kg)/(m^(3)))*(10^(3) \, (g)/(kg) )*( (1)/(10^(6)) \, (m^(3))/(cm^(3)) }) = 1.6315 * 10^(6) \, (g)/(cm^(3))`

Answer: 1.6315 x 10⁶ g/cm³