Find the density of the earth if its mass is 6×10^3kg and radius is 6.4×10^3km
density = mass/volume, so
(6×10^3 kg) / (4π/3 * (6.4×10^3 km)^3)
If you do the division, you will see an unexpectedly small result
You sure the mass of the earth is only 6 metric tons?
To find the density of the Earth, we can use the formula:
Density = Mass / Volume
The mass of the Earth is given as 6 × 10^24 kg. The volume of a sphere can be calculated using the formula:
Volume = (4/3) × π × r^3
In this case, the radius of the Earth is given as 6.4 × 10^6 km or 6.4 × 10^3 km (since 1 km = 10^3 meters).
So, let's convert the radius to meters:
Radius = 6.4 × 10^3 km × 10^3 m/km = 6.4 × 10^6 m
Now we can calculate the volume:
Volume = (4/3) × π × (6.4 × 10^6 m)^3
Using the value of π as approximately 3.14159, the calculation becomes:
Volume = (4/3) × 3.14159 × (6.4 × 10^6 m)^3
Volume ≈ 1.083 × 10^21 m^3
Now let's calculate the density using the given mass and the calculated volume:
Density = 6 × 10^24 kg / (1.083 × 10^21 m^3)
Density = 5.53 × 10^3 kg/m^3
Therefore, the density of the Earth is approximately 5.53 × 10^3 kg/m^3.
To find the density of the Earth, we can use the formula for density:
Density = Mass / Volume
Given that the mass of the Earth is 6 × 10^24 kg and the radius is 6.4 × 10^6 km, we need to find the volume of the Earth.
The volume of a sphere is given by the formula:
Volume = (4/3) × π × radius^3
Let's calculate the volume of the Earth first:
Radius = 6.4 × 10^6 km
Radius in meters = Radius × 1000 (since 1 km = 1000 m)
Radius in meters = 6.4 × 10^6 km × 1000 = 6.4 × 10^9 m
Volume = (4/3) × π × (6.4 × 10^9)^3
Now, we can substitute the values into the formula to find the volume.
Volume = (4/3) × 3.14159 × (6.4 × 10^9)^3
Calculating this, we get the volume of the Earth.
Next, we can substitute the mass and the volume into the formula for density:
Density = Mass / Volume
Density = (6 × 10^24 kg) / (calculated volume)
Calculating this division will give us the density of the Earth.