The radius of the earth is 6.37*10^6 m and its mass is 5.975*10^24 kg. Find the earth's average density to appropriate significant figure.
To find the average density of the Earth, we need to divide the mass of the Earth by its volume. Density is defined as mass divided by volume, so we can use the formula:
Density = Mass / Volume
First, let's calculate the volume of the Earth using its radius. The formula for the volume of a sphere is:
Volume = (4/3) * π * r^3
Given the radius of the Earth, we can plug in the values and calculate the volume:
Volume = (4/3) * π * (6.37 * 10^6)^3
Next, we divide the mass of the Earth by its volume to find the density:
Density = Mass / Volume
Given the mass of the Earth, we can plug in the values and calculate the density:
Density = 5.975 * 10^24 kg / Volume
Finally, round the density to the appropriate significant figure. Since the radius of the Earth is given to two significant figures, we round the density to two significant figures as well.
Lets plug in the values and calculate the density:
Density = 5.975 * 10^24 kg / Volume
Density = 5.975 * 10^24 kg / [(4/3) * π * (6.37 * 10^6)^3]
After calculating the volume and performing the division, we round the result to the appropriate significant figure to find the average density of the Earth.