We have a cube with a surface area of 24, which means each side has an area of 4. Therefore, the length of each side is 2. If we double the height, the volume becomes .

The equation for surface area of the original cube is 6s². If the sides all double in length the new equation is 6(2s)² or 6 * 4s². This makes the new surface area 4x that of the old. 4x10 = 40m²

Write the formula for the surface area of a cube.

Substitute the side.

The surface area of a cube can be calculated by squaring the sidelength and multiplying by six. The two smallest cubes therefore have surface areas

and

The surface areas form an arithmetic sequence with these two surface areas as the first two terms, so their common difference is 

.

The surface area of the largest, or sixth-smallest, cube, is

To solve, simply use the formula for the surface area of a cube. Thus,

To find the surface area of a cube means to find the area around the entire object. In the case of a cube, we will need to find that area of all the sides and the top and bottom. Since a cube has equal side lengths, the area of each side and the area of the top and bottom will all be the same.

Recall that the area for a side of a cube is:

From here there are two approaches one can take.

Approach one:

Add all the areas together.

Approach two:

Use the formula for the surface area of a cube,

In this particular case we are given the side length is 3.

Thus we can find the surface area to be,

by approach one,

and by appraoch two,

.

To solve, simply use the formula for the surface area of a cube.

If you do not remember the formula for the test, it is important to draw a picture or to visually conceptualize it. Remember, when finding area of a square or rectangle, you simply multiply the two side lengths. So for a cube in 3 dimensions, you simply have to multiply those three together.

However, a cube is a special case where all three lengths are the same. Thus,

First, we need the side length of the cube. Given that , where is a side length, we can solve for  and set  simply by taking the cube root of both sides.

Then we need to remember or realize that the surface area of a cube is because there will be six identical square faces. Plugging in , we get as our answer.

To solve, simply use the formula for the surface area of a cube.

If this is not a formula you have committed to memory, remember that a cube has 6 faces with equal area. So, start by calculating the surface area of one side (64) and add it 6 times. Thus,

You own a Rubik's cube with a volume of . What is the surface area of the cube?

To solve for edge length, think of the volume of a cube formula:

Now, we have the volume, so just rearrange it to solve for side length:

Next, recall the surface area of a cube formula:

Plug in and simplify to get: