Cubes - Math

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:

Using the volume given, we take it's cube to find the length of the cube: cm.

Therefore, the length of the cube is 8 cm.

Knowing the properties of a cube, this implies that the width and height of the cube is also 8 cm.

Since all sides are identical, the formula for the surface area is length times width times the number of sides: .

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

Substitute and solve.

Write the formula for the surface area of a cube, substitute the length provided in the question, and simplify.

The formula for the surface area of a cube is:

, where is the length of one side of the cube.

We are given the length of one side of the cube in question, so we can substitute that value into the surface area equation and solve:

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:

We first need to know the edge length before we can solve for surface area. Since we are provided the volume and all edges are of equal length, we can use the formula for volume to get the length of sides:

Now that we know the length of sides, we can plug this value into our surface area formula:

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

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

To find the surface area of a cube, square the length of one edge and multiply the result by six:

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

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.

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

The formula for the surface area of a cube is:

The surface area of the cube is

A cube has 6 faces. The area of each face is found by squaring the length of the side.

5times 5 = 25

Multiply the area of one face by the number of faces to get the total surface area of the cube.

25 times 6=150

To find the surface area of a cube, we must count the number of surface faces and add the areas of each together. In a cube there are faces, each a square with the same side lengths. In this example the side length is .

The area of a square is given by the equation . Using our side length, we can solve the area of once face of the cube.

We then multiply this number by , the number of faces of the cube to find the total surface area.

Our answer for the surface area is .

To find the surface area of a cube we must count the number of surface faces and add the areas of each of them together.

In a cube there are 6 faces, each a square with the same side lengths.

In this example the side lengths is 15 so the area of each square would be

We then multiply this number by 6, the number of faces of the cube, to get

Our answer for the surface area is .

By the Pythagorean Theorem,

The surface area of a cube having 6 sides, is 6 times the area of one of its sides.

The area of any side of a cube is the square of the side length.

So if the side length is , the area of any side is , or .

Thus the surface area of the cube is

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

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

However, all units must be the same. All of the units of this problem are in inches with the exception of .

Convert to inches.

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

If you calculated the surface area to equal , then you utilized the volume formula of a rectangular prism, which is ; 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: .

Rearrange an solve for .

Now, solve for the area of the cube using the formula .

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 .