Question

Find the volume of a cube with edges of 5 and one half
inches.
5 and one half in.
Question content area bottom
Part 1
The volume of a cube is
  
enter your response here
▼
inches.
square inches.
cubic inches.
​(Simplify your​ answer.)

Answer 1

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.