A star is estimated to have a mass of 2 X 10^36 kg. Assuming it to be a sphere of average radius 7.o X 10^5 km. Calculate the average density of the star in units of grams per cubic centimeter
Why did the star go on a diet? Because it wanted to maintain its "light" figure!
Now, let's calculate the average density of the star. To do that, we'll first need to convert the mass and radius into grams and centimeters, respectively.
Given:
Mass of the star = 2 x 10^36 kg
Radius of the star = 7.0 x 10^5 km
Converting the mass:
1 kg = 1000 grams
Therefore, the mass of the star in grams = 2 x 10^36 kg × 1000 grams/kg
Converting the radius:
1 km = 100,000 centimeters
Therefore, the radius of the star in centimeters = 7.0 x 10^5 km × 100,000 cm/km
Now, we can calculate the volume of the star using the formula:
Volume = (4/3)πr^3
Plugging in the values and calculating the volume:
Volume = (4/3)π × (7.0 x 10^5 cm)^3
Now, to find the average density, we divide the mass by the volume:
Density = mass/volume
Dividing the mass by the volume we calculated will give us the average density of the star in grams per cubic centimeter.
To calculate the average density of the star, we need to divide its mass by its volume.
Step 1: Convert the mass from kilograms to grams.
1 kilogram (kg) = 1000 grams (g)
2 X 10^36 kg = 2 X 10^36 kg * 1000 g/kg = 2 X 10^39 g
Step 2: Convert the radius from kilometers to centimeters.
1 kilometer (km) = 100,000 centimeters (cm)
7.0 X 10^5 km = 7.0 X 10^5 km * 100,000 cm/km = 7.0 X 10^10 cm
Step 3: Calculate the volume of the star.
The volume of a sphere is given by the formula:
V = 4/3 * π * r^3
V = 4/3 * 3.14 * (7.0 X 10^10 cm)^3
V ≈ 4/3 * 3.14 * (7.0 X 10^10)^3 cm^3
V ≈ 4/3 * 3.14 * (343 x 10^30) cm^3
V ≈ 4/3 * 3.14 * 343^3 * 10^30 cm^3
V ≈ 4/3 * 3.14 * 41816147 * 10^30 cm^3
V ≈ 4.19 * 10^40 cm^3
Step 4: Calculate the average density of the star.
Density (ρ) = Mass (m) / Volume (V)
Density = 2 X 10^39 g / 4.19 * 10^40 cm^3
Density ≈ 0.478 g/cm^3
Therefore, the average density of the star is approximately 0.478 grams per cubic centimeter.
To calculate the average density of the star, we need to know its mass and volume. Given the mass of the star (2 × 10^36 kg) and assuming it to be a sphere with an average radius of 7.0 × 10^5 km, we can follow these steps:
Step 1: Convert the radius from kilometers to centimeters.
1 km = 100,000 cm.
So, the radius of the star in centimeters is: 7.0 × 10^5 km × 100,000 cm/km = 7.0 × 10^5 × 10^5 cm = 7.0 × 10^10 cm.
Step 2: Calculate the volume of the star using the formula for the volume of a sphere.
The volume of a sphere is given by the formula: V = (4/3)πr^3.
In this case, the radius (r) is 7.0 × 10^10 cm.
Substituting the values into the formula, we get: V = (4/3)π(7.0 × 10^10)^3 cm^3.
Step 3: Simplify the equation and calculate the volume.
V = (4/3) × 3.1416 × (7.0 × 10^10)^3 cm^3.
V ≈ 1.437π × 3.43 × 10^31 cm^3.
V ≈ 4.936 × 10^31 cm^3.
Step 4: Calculate the density using the formula for density.
Density = mass/volume.
The mass of the star is given as 2 × 10^36 kg. We need to convert this to grams for consistency.
1 kg = 1000 grams, so 2 × 10^36 kg = 2 × 10^36 × 1000 grams.
Mass ≈ 2 × 10^39 grams.
Substituting the values into the density formula:
Density = mass/volume = (2 × 10^39 grams) / (4.936 × 10^31 cm^3).
Step 5: Simplify the equation and calculate the density.
Density ≈ 2 × 10^39 / 4.936 × 10^31 grams/cm^3.
Density ≈ 4.05 × 10^7 grams/cm^3.
Therefore, the average density of the star is approximately 4.05 × 10^7 grams per cubic centimeter.
Since you want density unit in g/cc, I would adjust the starting units, like so.
7.0 x 10^5 km = 1.0 x 10^10 cm (It's easier to do this at the start than at the end for me.)
The volume of a sphere is (4/3)*pi*r3 = ?? cc
Then mass = volume x density.
Convert mass to grams and solve for density.