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:
$\displaystyle x^3=V$

$\displaystyle x^3=64$

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

$\displaystyle x=4$

There is a sculpture in front of town hall which is shaped like a cube. If it has a volume of  $\displaystyle 343ft^3$, what is the length of one side of the cube?

To find the side length of a cube from its volume, simply use the following formula:

$\displaystyle V_{cube}=s^3$

Plug in what is known and use some algebra to get our answer:

$\displaystyle s=\sqrt[3]{343ft^3}=7ft$

You have a cube with a volume of $\displaystyle 125 m^3$. What is the cube's side length?

If we begin with the formula for volume of a cube, we can work backwards to find the side length.

$\displaystyle V_{cube}=s^3$

$\displaystyle 125m^3=s^3$

$\displaystyle s=\sqrt[3]{125m^3}=5m$

Making our answer:

$\displaystyle 5m$

The surface area of a cube is six times the square of the length of each edge, which here is $\displaystyle x- 7$. Therefore,

$\displaystyle 6s^{2} = A$

Substituting, then solving for $\displaystyle x$:

$\displaystyle 6 (x-7)^{2} = 486$

$\displaystyle 6 (x-7)^{2} \div 6 = 486 \div 6$

$\displaystyle (x-7)^{2} = 81$

$\displaystyle \sqrt{(x-7)^{2} }= \sqrt{81}$

Since the sidelength is positive, 

$\displaystyle x- 7 = 9$

$\displaystyle x = 16$

You have a crate with equal dimensions (height, length and width). If the volume of the cube is $\displaystyle 216 m^3$, what is the length of one of the crate's dimension?

Let's begin with realizing that we are dealing with a cube. A crate with equal dimensions will have equal height, length, and width, so it must be a cube.

With that in mind, we can find our side length by starting with the volume and working backward.

$\displaystyle V=s^3$

So, to find our side length, we just need to take the cubed root of the volume.

$\displaystyle s=\sqrt[3]{216m^3}=6m$

So, our answer is 6 meters, a fairly large crate!

Write the formula to find the volume of a cube.

$\displaystyle V=s^3$

Substitute the volume into the equation.

$\displaystyle 30=s^3$

Cube root both sides.

$\displaystyle \sqrt[3]{30}=\sqrt[3]{s^3}$

The answer is:  $\displaystyle \sqrt[3]{30}$