Answer:
Comparison:
Explanation:
To find the volumes of the two samples of uranium alloy, you must use the formula of density:
[tex]Density=\dfrac{mass}{volume}\\\\\\Volume=\dfrac{mass}{density}[/tex]
a) Critical mass of 49 kg
First, notice that 18.75g/cm³ is the same that 18.75 kg/dm³ (to convert from grams to kg you must divide by 1,000, and to convert from cm³ to dm³ you must divide by 1,000; thus, dividing both numerator an denominator by the same number leaves the fraction unchanged).
Now you can compute:
[tex]Volume=\dfrac{49kg}{18.75kg/dm^3}=2.6dm^3[/tex]
You can convert to cm³ multiplying by 1,000cm³/dm³.
Thus, volume = 2,600 cm³.
b) Critical mass = 16 kg
[tex]Volume=\dfrac{16kg}{18.75kg/dm^3}=0.85dm^3[/tex]
Volume = 850cm³
Compare with approximate volumes of a baseball, a volleyball, and a basketball:
You can calculate those volumes by using the formula for the volume of a sphere:
[tex]Volume=\dfrac{4}{3}\pi\times radius^3[/tex]
For the baseball: radius ≈ 3.75cm
[tex]Volume=\dfrac{4}{3}\pi\times (3.75cm)^3\approx 221cm^3[/tex]
For the basketball radius ≈ 12.0 cm
[tex]Volume=\dfrac{4}{3}\pi\times (12.0cm)^3approx 221cm^3\approx 7,238cm^3[/tex]
Thus, the comparison of the volumes is:
Baseball < Crittical mass 16 kg of Uranium 16 kg < Critical mass 49 kg of Uranium < Basketball
