the Earth has mass of approximately
5.98* 10^24kg and radius 6.38* 10^6m. what is the density of the Earth in (a)g/cm^3 and (b) kg/m^3 ?
tarob
To calculate the density of the Earth, we use the formula:
Density = Mass / Volume
First, let's calculate the volume of the Earth.
The formula for the volume of a sphere is given by:
Volume = (4/3) * pi * radius^3
Given that the radius of the Earth is 6.38 * 10^6 m, we can plug this value into the formula to calculate the volume.
Volume = (4/3) * 3.14 * (6.38 * 10^6)^3
Now, let's calculate the density using the given mass of the Earth.
Density = Mass / Volume
(a) To convert from kg/m^3 to g/cm^3, we need to divide the density by 1000.
(b) To convert from g/cm^3 to kg/m^3, we need to multiply the density by 1000.
Now, let's calculate the density of the Earth:
Step 1: Calculate the volume of the Earth
Volume = (4/3) * 3.14 * (6.38 * 10^6)^3
Step 2: Calculate the density
Density = Mass / Volume
Step 3: Convert the density to g/cm^3 and kg/m^3
(a) Density (g/cm^3) = Density / 1000
(b) Density (kg/m^3) = Density * 1000
Let's calculate the density:
Step 1:
Volume = (4/3) * 3.14 * (6.38 * 10^6)^3
Volume = 1.084 * 10^21 m^3
Step 2:
Density = Mass / Volume
Density = 5.98 * 10^24 kg / 1.084 * 10^21 m^3
Density = 5.51 * 10^3 kg/m^3
Step 3:
(a) Density (g/cm^3) = Density / 1000
Density (g/cm^3) = 5.51 * 10^3 kg/m^3 / 1000
Density (g/cm^3) = 5.51 g/cm^3
(b) Density (kg/m^3) = Density * 1000
Density (kg/m^3) = 5.51 * 10^3 kg/m^3 * 1000
Density (kg/m^3) = 5.51 * 10^6 kg/m^3
Therefore, the density of the Earth is (a) 5.51 g/cm^3 and (b) 5.51 * 10^6 kg/m^3.
To find the density of the Earth, we need to use the formula for density:
Density = Mass / Volume
To calculate the density of the Earth, we need to find the volume of the Earth first. We can use the formula for the volume of a sphere:
Volume = (4/3) * π * r^3
where r is the radius of the Earth.
Let's start by calculating the volume of the Earth:
Volume = (4/3) * π * (6.38*10^6)^3
Now we can substitute the values and calculate:
Volume ≈ (4/3) * 3.14159 * (6.38 * 10^6)^3
Volume ≈ 1.086 * 10^21 m^3
Now that we have the volume of the Earth, we can calculate its density.
(a) To find the density of the Earth in g/cm^3, we need to convert the mass from kg to g and the volume from m^3 to cm^3.
Density in g/cm^3 = (Mass in g) / (Volume in cm^3)
= (5.98 * 10^24 kg) * (1000 g/kg) / (1.086 * 10^21 m^3) * (100^3 cm^3/m^3)
= (5.98 * 10^27 g) / (1.086 * 10^21 * 10^6 cm^3)
≈ 5.51 g/cm^3
Therefore, the density of the Earth is approximately 5.51 g/cm^3.
(b) To find the density of the Earth in kg/m^3, we don't need to make any conversions.
Density in kg/m^3 = Mass / Volume
= (5.98 * 10^24 kg) / (1.086 * 10^21 m^3)
≈ 5.51 * 10^3 kg/m^3
Therefore, the density of the Earth is approximately 5.51 * 10^3 kg/m^3.
volume = (4/3)*pi*r^3 in units of m^3
density = mass/volume = ? in kg/m^3
Convert kg to g and m^3 to cm^3 for the other units.