# Intermediate Geometry : Cubes

## Example Questions

### Example Question #31 : Solid Geometry

The volume of a cube is .

What is the surface area of the cube?

Explanation:

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: .

### Example Question #32 : Solid Geometry

If a side of a cube has a length of , what is the cube's surface area?

Explanation:

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

Substitute and solve.

### Example Question #33 : Solid Geometry

Find the surface area of a cube with a side length of .

Explanation:

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

### Example Question #991 : Intermediate Geometry

if the side length of a cube is , what is the cube's surface area?

Explanation:

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:

### Example Question #35 : Solid Geometry

A cube has a sphere inscribed inside it  with a diameter of 4 meters. What is the surface area of the cube?

None of these

Explanation:

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:

### Example Question #31 : Solid Geometry

A geometric cube has a volume of . Find the surface area of the cube.

Explanation:

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:

### Example Question #2 : How To Find The Volume Of A Cube

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Explanation:

If we let  represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of  is 27 times as large as the small cube's volume of .

### Example Question #37 : Solid Geometry

The side length of a cube is  inches.

What is the volume?

Explanation:

The volume of a cube is

So with a side length of 7 inches, the volume is

### Example Question #1 : How To Find The Volume Of A Cube

The side length of a cube is  ft.

What is the volume?

Explanation:

The volume of a cube is

So with a side length of 2 ft, the volume is

### Example Question #1 : How To Find The Volume Of A Cube

Find the volume of a cube with an edge length of