As mentioned before, our asteroid is in the shape of a sphere and has a mass of 2000 kilograms. Determine the density (in grams per cubic centimeter) of this asteroid if its diameter is known to be 1.2 meters.
To determine the density of the asteroid, we need to use the formula: Density = Mass / Volume.
First, let's convert the mass from kilograms to grams. Since 1 kilogram is equal to 1000 grams, the mass of the asteroid is 2000 * 1000 = 2,000,000 grams.
Next, we need to calculate the volume of the sphere. The formula for the volume of a sphere is V = (4/3) * π * r^3, where π is approximately equal to 3.14159 and r is half the diameter of the sphere.
Given that the diameter is 1.2 meters, the radius (r) would be 1.2/2 = 0.6 meters.
Now we can substitute the values into the volume formula:
V = (4/3) * π * (0.6)^3
V = (4/3) * 3.14159 * 0.216
V = 0.904777 meters cubed
Finally, we can calculate the density using the formula:
Density = Mass / Volume
Density = 2,000,000 grams / 0.904777 meters cubed
Density ≈ 2,209,607 grams per meter cubed
To convert this into grams per cubic centimeter (g/cm³), we need to convert meters cubed (m³) to cubic centimeters (cm³).
1 meter cubed (m³) is equal to 1,000,000 cubic centimeters (cm³), so:
Density ≈ 2,209,607 grams / (0.904777 * 1,000,000) cm³
Density ≈ 2.44 grams per cubic centimeter (g/cm³)
Therefore, the density of the asteroid is approximately 2.44 grams per cubic centimeter.