The critical mass can be decreased to 16 kg if the alloy is surrounded by a layer of natural uranium (which acts as a neutron reflector). What is the volume of such smaller mass? Compare your answers to the approximate volumes of a baseball, a volleyball, and a basketball.

The question is not complete and the first part missing is;

A particular uranium alloy has a density of 18.75 g/cm³. Please answer the following questions below, providing the explanation to your answers.

a. What volume is occupied by a critical mass of 49 kg of this alloy?

A) 2610 cm³

B) Mbase < Ma < Mv < Mbask

Explanation:

a) density of uranium alloy = 18.75 g/cm³ = 18750 kg/m³

Mass (m) = 16kg

We know that;

volume = mass / density

Thus, volume = 49kg / 18750kg/m³ = 2.61 x 10^(-3) m³ = 2610 cm³

b) Mass is now reduced to 16kg instead of 49kg. Thus,

Volume = 16/18750 = 0.000853 m³ or 853 cm³

From research, the diameters of baseball, volleyball and basketball are;

Baseball = 7.5 cm

Volleyball = 21.3 cm

Basketball = 24.26cm

baseball:

Since diameter is about 7.5 cm

then V = πd³/6 = π(7.5³)/6 = 220.89 cm³

volleyball: diameter is around 21.3 cm³, then V =π(21.3³)/6 = 5059.86 cm³

basketball: diameter around 24.26, then V =π(25³)/6 = 8181.23 cm³

Lets call the Volume of Alloy Ma while Mass of Baseball is Mbase

Mass of volleyball is Mv while mass of basketball is Mbask.

So comparing the volumes, we have;

Mbase < Ma < Mv < Mbask