A star is estimated to have a mass of 1 ✕ 1036 kg. Assuming it to be a sphere of average radius 7.0 105 km, calculate the average density of the star in units of grams per cubic centimeter.

round to the correct number of significant figures.

Change radius of 7.0E5 km to cm; then (4/3)*pi*r^3 = volume of star.

Change mass 1E36 kg to g.
Density = mass/volume
Post your work if you get stuck.

910000

To calculate the average density of the star, we need to convert the given values to a common set of units.

1 kilogram (kg) = 1000 grams (g)
1 kilometer (km) = 100,000 centimeters (cm)

Given:
Mass of the star = 1 × 10^36 kg
Average radius of the star = 7.0 × 10^5 km

Step 1: Convert the mass of the star from kg to g
1 × 10^36 kg × 1000 g/kg = 1 × 10^39 g

Step 2: Convert the average radius of the star from km to cm
7.0 × 10^5 km × 100,000 cm/km = 7.0 × 10^10 cm

Step 3: Calculate the volume of the star using the formula for the volume of a sphere
Volume of a sphere = (4/3)π(radius)^3
Volume of the star = (4/3)π(7.0 × 10^10)^3 cm^3

Step 4: Calculate the average density of the star using the formula for density
Density = Mass/Volume

Density = (1 × 10^39 g) / [(4/3)π(7.0 × 10^10)^3 cm^3]

Step 5: Calculate the value of the expression

Density ≈ 0.527 g/cm^3

Therefore, the average density of the star is approximately 0.527 grams per cubic centimeter (g/cm^3).

To calculate 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:

Volume = (4/3) * π * (radius^3)

First, let's convert the given radius to meters:

Radius = 7.0 * 10^5 km * 10^3 m/km = 7.0 * 10^8 m

Now, let's calculate the volume of the star in cubic meters:

Volume = (4/3) * π * (7.0 * 10^8)^3

Next, we need to convert the mass of the star from kilograms to grams:

Mass = 1 * 10^36 kg * 10^3 g/kg = 1 * 10^39 g

Now, let's calculate the average density of the star in grams per cubic centimeter:

Density = Mass / Volume

Since 1 m^3 = 1 * 10^6 cm^3, we can convert the volume from cubic meters to cubic centimeters by multiplying by (1 * 10^6 cm^3/m^3):

Density = (1 * 10^39 g) / [(4/3) * π * (7.0 * 10^8 m)^3 * (1 * 10^6 cm^3/m^3)]

Now we can plug in the values and solve for the density:

Density = (1 * 10^39 g) / [(4/3) * π * (7.0 * 10^8)^3 * (1 * 10^6)]

Using a calculator and the value of π as 3.14159, we get:

Density ≈ 2.50 g/cm³

Therefore, the average density of the star is approximately 2.50 grams per cubic centimeter.