One of your holiday gifts is wrapped in a cube-shaped box. 

If one of the edges has a length of 6 inches, what is the volume of the box?

Find the volume of a cube via the following:

\(\displaystyle V_{cube}=s^3=(6in)^3=216in^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = a^3\)

where a is the length of any side of the cube.

Now, we know the height of the cube is 3in.  Because it is a cube, all sides (lengths, widths, height) are the same.  That is why we can find any length for the formula.  

Knowing this, we can substitute into the formula.  We get

\(\displaystyle V = (3\text{in})^3\)

\(\displaystyle V = 3\text{in} \cdot 3\text{in} \cdot 3\text{in}\)

\(\displaystyle V = 9\text{in}^2 \cdot 3\text{in}\)

\(\displaystyle V = 27\text{in}^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = l \cdot w \cdot h\)

where l is the length, w is the width, and h is the height of the cube.

Now, we know the length of the cube is 5cm.  Because it is a cube, all sides are equal.  Therefore, the width and the height of the cube are also 5cm.

Knowing this, we will substitute into the formula.  We get

\(\displaystyle V = 5\text{cm} \cdot5\text{cm} \cdot5\text{cm}\)

\(\displaystyle V = 25\text{cm}^2 \cdot 5\text{cm}\)

\(\displaystyle V = 125\text{cm}^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = l \cdot w \cdot h\)

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 8in.  Because it is a cube, all sides/lengths are equal.  Therefore, the length and width are also 8in.

Knowing this, we can substitute into the formula. We get

\(\displaystyle V = 8\text{in} \cdot 8\text{in} \cdot 8\text{in}\)

\(\displaystyle V = 64\text{in}^2 \cdot 8\text{in}\)

\(\displaystyle V = 512\text{in}^3\)

While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be \(\displaystyle 12 cm\). Find the cube's volume.

To find the volume of a cube, use the following formula:

\(\displaystyle V=s^3\)

\(\displaystyle V=(12cm)^3=1728cm^3\)

So our answer is

\(\displaystyle 1728 cm^3\)

You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the volume of your box be?

Begin with the formula for volume of a cube:

\(\displaystyle V=s^3\)

Where s is our side length and V is our volume.

Now, we need to plug in our side length and solve for V

\(\displaystyle V=(3ft)^3=3ft*9ft^2=27ft^3\)

So, our volume is 

\(\displaystyle 27ft^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = l \cdot w \cdot h\)

where l is the length, w is the width, and h is the height of the cube.

Now, we know the width is 9in.  Because it is a cube, all sides are equal.  Therefore, the length and the height are also 9in.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle V = 9\text{in} \cdot9\text{in} \cdot9\text{in}\)

\(\displaystyle V = 81\text{in}^2 \cdot 9\text{in}\)

\(\displaystyle V = 729\text{in}^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = l \cdot w \cdot h\)

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 8in.  Because it is a cube all sides (length, height, width) are the same.  So, all are 8in.

Now we can substitute.  We get

\(\displaystyle V = 8\text{in} \cdot 8\text{in} \cdot 8\text{in}\)

\(\displaystyle V = 512\text{in}^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = l \cdot w \cdot h\)

where l is the length, w is the width, and h is the height of the cube.

Now, we know the length of the cube is 5in.  Because it is a cube, all sides/lengths are equal.  Therefore, the length and width are also 5in.

Knowing this, we can substitute into the formula. We get

\(\displaystyle V = 5\text{in} \cdot 5\text{in} \cdot 5\text{in}\)

\(\displaystyle V = 25\text{in}^2 \cdot 5\text{in}\)

\(\displaystyle V = 125\text{in}^3\)

To find the volume of a cube, we will use the following formula:

\(\displaystyle V = l \cdot w \cdot h\)

where l is the length, w is the width, and h is the height of the cube. 

Now, we know the height of the cube is 14cm.  Because it is a cube, all sides (lengths, widths, heights) are equal.  Therefore, the length and the width are also 14cm.  So, we can substitute.  We get

\(\displaystyle V = 14\text{cm} \cdot14\text{cm} \cdot14\text{cm}\)

\(\displaystyle V = 14\text{cm} \cdot 196\text{cm}^2\)

\(\displaystyle V = 2744\text{cm}^2\)