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 surface area.

To find the surface area, use the following formula:

\(\displaystyle SA=6s^2=6(12cm)^2=864cm^2\)

A cube has all equal sides (length, width, height).  To find the surface area of a cube, we will use the following formula:

\(\displaystyle SA = 6a^2\)

Now, we know the base of the cube is 8in.  Because all sides are equal (i.e. all sides are 8in), we will use that to substitute into the formula.  We get

\(\displaystyle SA = 6 \cdot (8\text{in})^2\)

\(\displaystyle SA = 6 \cdot 64\text{in}^2\)

\(\displaystyle SA = 384\text{in}^2\)

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 surface area of your box be?

To find the surface area, use the formula:

\(\displaystyle SA=6s^2\)

Where s is our side length and SA is our surface area.

Plug in our known and simplify

\(\displaystyle SA=6 (3ft)^2=6*9ft^2=54ft^2\)

So, our answer is 

\(\displaystyle 54ft^2\)

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

\(\displaystyle SA = 6a^2\)

where a is the length of any side of the cube.  Because it is a cube, all sides are equal.  Therefore, we can use any side in the formula.

Now, we know the length of the cube is 11in.  We can substitute that into the formula.  We get

\(\displaystyle SA = 6 \cdot (11\text{in})^2\)

\(\displaystyle SA = 6 \cdot 121\text{in}^2\)

\(\displaystyle SA = 726\text{in}^2\)

To find the surface area of a cube, we will use the following formula.

\(\displaystyle SA = 6a^2\)

where a is the length of any side of the cube.  We can use any side because all sides have the same length on a cube.

Now, we know the width of the cube is 7cm.  So, we can substitute.  We get

\(\displaystyle SA = 6 \cdot (7\text{cm})^2\)

\(\displaystyle SA = 6 \cdot 49\text{cm}^2\)

\(\displaystyle SA = 294\text{cm}^2\)

To find the surface area of a cube, we will use the following formula.

\(\displaystyle SA = 6a^2\)

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

Now, we know the width of the cube is 7in.  Because it is a cube, all sides are equal (this is why we can use any length in the formula).  So, we will use 7in in the formula.  We get

\(\displaystyle SA = 6 \cdot (7\text{in})^2\)

\(\displaystyle SA = 6 \cdot 49\text{in}^2\)

\(\displaystyle SA = 294\text{in}^2\)

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

\(\displaystyle SA = 6 \cdot l \cdot w\)

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

Now, we know the width of the cube is 6in.  Because it is a cube, all lengths, widths, and heights are the same.  Therefore, the length is also 6in.

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

\(\displaystyle SA = 6 \cdot 6\text{in} \cdot 6\text{in}\)

\(\displaystyle SA = 6 \cdot 36\text{in}^2\)

\(\displaystyle SA = 216\text{in}^2\)

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

\(\displaystyle SA = 6 a^2\)

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

Now, we know the length of the cube is 9cm. So, we get

\(\displaystyle SA = 6 \cdot (9\text{cm})^2\)

\(\displaystyle SA = 6 \cdot 81\text{cm}^2\)

\(\displaystyle SA = 486\text{cm}^2\)

To find the surface area of a cube, we will use the following formula.

\(\displaystyle SA = 6a^2\)

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

Now, we know the width of the cube is 6cm.

So, we get

\(\displaystyle SA = 6 \cdot (6\text{cm})^2\)

\(\displaystyle SA = 6 \cdot 6\text{cm}^2\)

\(\displaystyle SA = 216\text{cm}^2\)

Let \(\displaystyle x\) be the length of an edge of the cube. The volume of a cube can be determined by the equation:
\(\displaystyle x^3=V\)

\(\displaystyle x^3=64\)

\(\displaystyle \sqrt[3]{x^3}=\sqrt[3]{64}\)

\(\displaystyle x=4\)