How to find the length of an edge of a cube - PSAT Math

In order to find the surface area of a cube, we need to solve for the length of each side, .

Recall the formula for volume:

Plug in what we know and solve for :

Now plug this value into the surface area formula:

The volume of a cube is length x width x height. Since it's a cube, though, the length, width, and height are all equal, and equivalent to the length of one edge of the cube. Therefore, to find the lenght of an edge of the cube, just find the cube root of the volume. In this case, the cube root of 512 is equal to 8.

All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power.

So if we take the edge of the cube to be of length x, then:

So the length of the edge of a cube with a volume of 125 is 5.

The formula for the volume of a cube is

where is the length of a side.

Here, the volume is 729. To find the side length, take the cube root of both sides:

The cube root of 729 is 9, so the length of each side of the cube is 9 feet.

The formula for the volume of a cube is where s is any edge.

This means one edge of the cube is . We then divide 8.5 by 12 to convert to feet.

feet.

The number of square units in the surface area of a cube is given by the formula 6s2, where s is the length of the side of the cube in units. Moreover, the number of cubic units in a cube's volume is equal to s3.

Since the number of square units in the surface area is twice as large as the cubic units of the volume, we can write the following equation to solve for s:

6s2 = 2s3

Subtract 6s2 from both sides.

2s3 – 6s2 = 0

Factor out 2s2 from both terms.

2s2(s – 3) = 0

We must set each factor equal to zero.

2s2 = 0, only if s = 0; however, no cube has a side length of zero, so s can't be zero.

Set the other factor, s – 3, equal to zero.

s – 3 = 0

Add three to both sides.

s = 3

This means that the side length of the cube is 3 units. The volume, which we previously stated was equal to s3, must then be 33, or 27 cubic units.

The answer is 27.

In order to find the surface area of a cube, we need to solve for the length of each side, .

Recall the formula for volume:

Plug in what we know and solve for :

Now plug this value into the surface area formula:

The volume of a cube is length x width x height. Since it's a cube, though, the length, width, and height are all equal, and equivalent to the length of one edge of the cube. Therefore, to find the lenght of an edge of the cube, just find the cube root of the volume. In this case, the cube root of 512 is equal to 8.

All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power.

So if we take the edge of the cube to be of length x, then:

So the length of the edge of a cube with a volume of 125 is 5.

The formula for the volume of a cube is

where is the length of a side.

Here, the volume is 729. To find the side length, take the cube root of both sides:

The cube root of 729 is 9, so the length of each side of the cube is 9 feet.

The formula for the volume of a cube is where s is any edge.

This means one edge of the cube is . We then divide 8.5 by 12 to convert to feet.

feet.

The number of square units in the surface area of a cube is given by the formula 6s2, where s is the length of the side of the cube in units. Moreover, the number of cubic units in a cube's volume is equal to s3.

Since the number of square units in the surface area is twice as large as the cubic units of the volume, we can write the following equation to solve for s:

6s2 = 2s3

Subtract 6s2 from both sides.

2s3 – 6s2 = 0

Factor out 2s2 from both terms.

2s2(s – 3) = 0

We must set each factor equal to zero.

2s2 = 0, only if s = 0; however, no cube has a side length of zero, so s can't be zero.

Set the other factor, s – 3, equal to zero.

s – 3 = 0

Add three to both sides.

s = 3

This means that the side length of the cube is 3 units. The volume, which we previously stated was equal to s3, must then be 33, or 27 cubic units.

The answer is 27.

In order to find the surface area of a cube, we need to solve for the length of each side, .

Recall the formula for volume:

Plug in what we know and solve for :

Now plug this value into the surface area formula:

The volume of a cube is length x width x height. Since it's a cube, though, the length, width, and height are all equal, and equivalent to the length of one edge of the cube. Therefore, to find the lenght of an edge of the cube, just find the cube root of the volume. In this case, the cube root of 512 is equal to 8.

All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power.

So if we take the edge of the cube to be of length x, then:

So the length of the edge of a cube with a volume of 125 is 5.

The formula for the volume of a cube is

where is the length of a side.

Here, the volume is 729. To find the side length, take the cube root of both sides:

The cube root of 729 is 9, so the length of each side of the cube is 9 feet.