Answer:
- a) Critical mass of 49 kg of Uranium: 2600 cm³
- b) Critical mass of 16 kg Uranium: 850 cm³
Comparison:
- Baseball < Critical mass of 16 kg of uranium < critical mass of 49 kg of uranium < basketball.
Explanation:
To find the volumes of the two <em>samples</em> of uranium alloy, you must use the formula of density:

<u>a) Critical mass of 49 kg</u>
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:

You can convert to cm³ multiplying by 1,000cm³/dm³.
Thus, volume = 2,600 cm³.
<u>b) Critical mass = 16 kg</u>

Volume = 850cm³
<u>Compare with approximate volumes of a baseball, a volleyball, and a basketball:</u>
You can calculate those volumes by using the formula for the volume of a sphere:

For the baseball: radius ≈ 3.75cm

For the basketball radius ≈ 12.0 cm

Thus, the comparison of the volumes is:
Baseball < Crittical mass 16 kg of Uranium 16 kg < Critical mass 49 kg of Uranium < Basketball