The surface area of a cube = 6a² where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a² → a² = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

In order to find the surface area of a cube, use the formula $\displaystyle SA=6(s^{2})$.

$\displaystyle SA=6*(7.2in)^{2}$

$\displaystyle SA=6*51.84in^{2}$

$\displaystyle SA=311.04in^{2}$

$\displaystyle \rightarrow 311in^{2}$

In order to find the surface area of a rectangular prism, use the formula $\displaystyle SA=(2*lw)+(2*wh)+(2*lh)$.

However, all units must be the same. All of the units of this problem are in inches with the exception of $\displaystyle \dpi{100} l=2.2ft$.

Convert to inches.

$\displaystyle l=\frac{2.2ft}{1}*\frac{12in}{1ft}$

$\displaystyle l=26.4in$

Now, we can insert the known values into the surface area formula in order to calulate the surface area of the rectangular prism.

$\displaystyle SA=(2*26.4in*18in)+(2*18in*14in)+(2*26.4in*14in)$

$\displaystyle SA=(950.4in^{2})+(504in^{2})+(739.2in^{2})$

$\displaystyle SA=2193.6in^{2}$

If you calculated the surface area to equal $\displaystyle 6652.8in^{2}$, then you utilized the volume formula of a rectangular prism, which is $\displaystyle V=l*w*h$; this is incorrect.

A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: $\displaystyle 1:\sqrt{2}$.

$\displaystyle \frac{s}{d}=\frac{1}{\sqrt{2}}$

$\displaystyle \dpi{100} \dpi{100} \frac{s}{4.2cm}=\frac{1}{\sqrt{2}}$

Rearrange an solve for $\displaystyle s$.

$\displaystyle \dpi{100} s=\frac{4.2cm}{\sqrt{2}}$

Now, solve for the area of the cube using the formula $\displaystyle \dpi{100} \dpi{100} SA=6(s^{2})$.

$\displaystyle SA=6*(\frac{4.2cm}{\sqrt{2}})^{2}$

$\displaystyle SA=\frac{6}{1}*(\frac{4.2cm}{\sqrt{2}}*\frac{4.2cm}{\sqrt{2}})$

$\displaystyle \dpi{100} SA=\frac{6}{1}*(\frac{17.64cm^{2}}{2})$

$\displaystyle \dpi{100} \dpi{100} SA=3*17.64cm^{2}$

$\displaystyle \rightarrow 52.92cm^{2}$

The surface area of a cube is the sum of the area of each face.  Since there are 6 faces on a cube, the surface area of the entire cube is $\displaystyle 6\cdot16$.

To find the surface area of a cube, square the length of one edge and multiply the result by six: $\displaystyle 6(a^{2})$

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

To find the surface of a cube, use the standard equation: 

$\displaystyle SA=6a^2$

where $\displaystyle a$ denotes the side length.

Plug in the given value for $\displaystyle a$ to find the answer:

$\displaystyle SA=6\cdot \left(\frac{3}{2}\right)^2=6\cdot \left(\frac{9}{4}\right)=\frac{27}{2}$

Remember, $\displaystyle 6\; in=0.50\; ft$.

For a cube:

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

Thus $\displaystyle 6(0.50)^{2}=6(0.25)=1.50\; ft^{2}$.

$\displaystyle \textup{Each of the six identical faces of the cube is a square with sides }p.$

$\displaystyle \textup{Each face: }A=p^{2}\: \: \: \: \: \textup{Surface area}=6p^{2}$

The formula for the surface area of a cube is

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

where $\displaystyle s$ is the length of the side.

Plugging in our values, we get:

$\displaystyle SA=6(4\ m)^2$

$\displaystyle SA=96\ m^2$