if a T. rex has a mass of 6.8 metric tons and a density of 0.8 g/cm^3 then calculate the volume of its body in cubic meters.
To calculate the volume of the T. rex's body, we need to convert its mass from metric tons to grams and its density from g/cm^3 to g/m^3.
1 metric ton is equal to 1,000 kilograms, and 1 kilogram is equal to 1,000 grams. So, the T. rex's mass can be converted to grams by:
Mass in grams = Mass in metric tons × 1,000,000
Mass in grams = 6.8 metric tons × 1,000,000 = 6,800,000 grams
Next, we need to convert the density from g/cm^3 to g/m^3. Since there are 100 centimeters in a meter, we can convert the density by multiplying it by 100³:
Density in g/m^3 = Density in g/cm^3 × (100 cm/m)^3
Density in g/m^3 = 0.8 g/cm^3 × (100 cm/m)^3 = 0.8 g/cm^3 × 1,000,000 g/m^3 = 800,000 g/m^3
Now that we have the mass in grams and the density in g/m^3, we can calculate the volume using the formula:
Volume = Mass / Density
Volume = 6,800,000 g / 800,000 g/m^3 = 8.5 cubic meters
Therefore, the volume of the T. rex's body is 8.5 cubic meters.