The area of one face is given by the length of a side squared.

$\displaystyle A_{face}=(3cm)^2=9\ cm^2$

The area of 6 faces is then given by six times the area of one face: 54 cm².

$\displaystyle A_{total}=6(A_{face})=6(9\ cm^2)=54\ cm^2$

We must first find the radius of the sphere in order to solve this problem. Since we already know the volume, we will use the volume formula to do this.

$\displaystyle V_{sphere}=\frac{4}{3}\pi r^{3}$

$\displaystyle \frac{32}{3}\pi =\frac{4}{3}\pi r^{3}$

$\displaystyle \frac{32}{3}=\frac{4}{3}r^{3}$

$\displaystyle \frac{3}{4}\cdot \frac{32}{3}= r^{3}$

$\displaystyle 8=r^{3}$

$\displaystyle r=2$

With the radius of the sphere in hand, we can now apply it to the cube. The radius of the sphere is half the distance from the top to the bottom of the cube (or half the distance from one side to another). Therefore, the radius represents half of a side length of a square. So in this case

$\displaystyle side=2\cdot 2=4$

The formula for the surface area of a cube is:

$\displaystyle SA_{cube}=6s^{2}$

$\displaystyle 6s^{2}=6\cdot (4)^{2}=6\cdot 16=96$

The surface area of the cube is $\displaystyle 96\ m^{2}$

To answer this question, we need to find the surface area of a cube.

To do this, we must find the area of one face and multiply it by $\displaystyle 6$, because a cube has $\displaystyle 6$ faces that are square in shape and equal in size. 

To find the area of a square, you multiply its length by its width. (Note that the length and width of a square are the same.) Therefore, for this data:

$\displaystyle area = L\cdot W=4\:in\cdot 4\:in=16\:in^2$

We now must multiply the area of one face by 6 to get the total surface are of the cube.

$\displaystyle 16\:in^2\cdot6=96\:in^2$

Therefore, the surface are of a four-inch cube is $\displaystyle 96\:in^2$.

First we need to find the side length of the cube. Do that by taking the cube root of the volume.

$\displaystyle \sqrt[n]{512mm^3}$ = $\displaystyle 8mm$
Next plug the side length into the formula for the surface area of a cube:

$\displaystyle SA = 6*s^2 = 6 *(8mm)^2 = 384mm^2$

The surface area of a cube is a measure of the total area of the surface of all of the sides of that cube.

Since a cube contains $\displaystyle 6$ square sides, the surface area is $\displaystyle 6$ times the area of a square side.

The area of one square side is sidelength $\displaystyle x$ sidelength, or $\displaystyle 4*4 = 16$ in this case. Therefore, the surface area of this cube is $\displaystyle 16*6 = 96$ square inches.

To find the side length of a cube whose surface area is the same as its volume, set the surface area and volume equations of a cube equal to each other, the solve for the side length:

$\displaystyle V=s^3: SA=6a^2$

Set these two formulas equal to eachother and solve for s.

$\displaystyle \\ s^3 = 6*s^2 \\ \newline \frac{s^3}{s^2}=\frac{6*s^2}{s^2}\\ \newline s = 6$

To find the surface area of a cube with a given side length, $\displaystyle s$ use the formula:
$\displaystyle SA = 6s^2 = 6*3^2 = 6*9 = 54$

To find surface area of a cube, simply calculate the area of one side and multiply it by $\displaystyle 6$. Thus,

 $\displaystyle SA=s^2*6=4^2*6=16*6=96$

To find surface aarea, simply multiply the area of a face by 6 since there are 6 faces. Thus,

$\displaystyle SA=6\cdot s^2=6\cdot3^2=6\cdot9=54$

To solve, simply multiply the face area by $\displaystyle 6$. Thus,

$\displaystyle SA=s^2*6=1^2*6=6$