Final answer:
To find the average density of a star, you must first convert mass and radius to grams and centimeters, respectively, calculate the volume using the volume formula for a sphere, and then divide mass by volume to get density. The calculated density for the given star is approximately 0.87 g/cm³.
Step-by-step explanation:
To calculate the average density of the star, we will first convert all units to cgs (centimeters, grams, seconds) as these are the standard units for density. The mass of the star is given as 1 × 1036 kg, which we convert to grams (1 kg = 1000 g), giving us 1 × 1039 g. The radius is given in kilometers (1 km = 105 cm), so 6.5 × 105 km becomes 6.5 × 1010 cm. The volume of a sphere is given by the formula V = (4/3)πr3, where r is the radius in centimeters.
Plugging in the radius, we get V = (4/3)π(6.5 × 1010 cm)3 or approximately 1.15 × 1033 cm3. Now, we can find the density (ρ) using the formula ρ = mass/volume. This gives us ρ = (1 × 1039 g) / (1.15 × 1033 cm3) which is approximately 0.87 g/cm3. This is the average density of the star.