To find the volume of a cube, you can use the formula:
\[ V = s^3 \]
where \( V \) is the volume and \( s \) is the length of an edge of the cube.
In this case, the edge length is 5 and one half inches, which can be expressed as a mixed number:
\[ s = 5 \frac{1}{2} = 5.5 \quad \text{or} \quad s = \frac{11}{2} \text{ inches} \]
Now we will calculate the volume:
\[ V = \left(\frac{11}{2}\right)^3 = \frac{11^3}{2^3} = \frac{1331}{8} \text{ cubic inches} \]
Now simplify or convert if necessary:
To do the division, \( 1331 \div 8 = 166.375 \), which can be expressed as:
\[ V = 166 \frac{3}{8} \text{ cubic inches} \]
Thus, the volume of the cube is:
\[ \frac{1331}{8} \text{ cubic inches} \]
or
\[ 166 \frac{3}{8} \text{ cubic inches} \]
Final Answer:
The volume of the cube is \( \frac{1331}{8} \) cubic inches or approximately \( 166.375 \) cubic inches.