Step 1. To find the volume of a cube, we use the following formula:
![V=s^3](https://img.qammunity.org/2023/formulas/mathematics/college/s99b7yex3i2xgsinpjj9mnjujocnckvvdc.png)
Where V is the volume and s is the length of the side of the cube.
In this case:
![s=(3)/(8)km](https://img.qammunity.org/2023/formulas/mathematics/college/rpop0jc8zkru1onyq4lboihjdz4skd2xt3.png)
Step 2. Substituting the value of s into the formula:
![V=((3)/(8)km)^3](https://img.qammunity.org/2023/formulas/mathematics/college/jf8f0cjwhhhbgld1exhorqm6ijjip3x8na.png)
This can be simplified as follows:
![V=(3^3)/(8^3)km^3](https://img.qammunity.org/2023/formulas/mathematics/college/68z0n191jl17n17b0osi1i51z6s8r4bogs.png)
Calculating 3^3 is 3x3x3=27 and 8^3 is 8x8x8=512, thus:
![V=(27)/(512)km^3](https://img.qammunity.org/2023/formulas/mathematics/college/qtuh2j0pphyknssa3ziv4204m7u75awcow.png)
This is the solution represented as an improper fraction.
Answer:
![(27)/(512)\text{ cubic kilometers}](https://img.qammunity.org/2023/formulas/mathematics/college/2sp4sjfwgkryik2cjwf8yv5fkdu6y03ild.png)