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

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 .

To find the surface area of a cube, we find the area of a face by multiplying two of its sides together; then, we multiply by , since a cube has six faces. So, if is the length of one side of a cube, then the cube's surface area can be represented as .

We know that for this problem, , so we can substitute this value into the equation and solve for the cube's surface area:

To solve this, first calculate the side length based on the volume given. Recall that the equation for the volume of a cube is:

, where is the side length.

For our data, this gives us:

Taking the cube-root of both sides, we get:

Now, use the surface area formula to compute the total surface area:

, where is the length of a side of the cube. This equation is easy to memorize because it is merely a multiplication of a single side () by because a cube has equal sides.

For our data, this gives us:

To solve this, first calculate the side length based on the volume given. Recall that the equation for the volume of a cube is:

, where is the side length.

For our data, this gives us:

Taking the cube-root of both sides, we get:

(You will need to use a calculator for this. If your calculator gives you something like . . . it is okay to round. This is just the nature of taking roots!).

Now, use the surface area formula to compute the total surface area:

, where is the length of a side of the cube. This equation is easy to memorize because it is merely a multiplication of a single side () by because a cube has equal sides.

For our data, this gives us:

In order to find the surface area of a cube, use the formula .

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

where denotes the side length.

Plug in the given value for to find the answer:

Since the sphere is inscribed within the cube, its diameter is the same length as an edge of the cube. Since cubes have identical side lengths we find the area of one side and then multiply by the number of sides to find the total surface area.

Area of one side:

Total surface area:

Write the formula to find the surface of a cube, where is the length.

Substitute and solve.