DSQ: Calculating the length of an edge of a cube - GMAT Quantitative

Call the sidelength, surface area, and volume of the cube , , and , respectively.

Then

or, equivalently,

So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be

Also,

or, equivalently,

Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be

Therefore, the answer is that either statement alone is sufficient.

The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula can be used to find the volume of the sphere.

In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.

Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is where is the length of an edge of the cube and is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.

Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.

Statement 1 alone is sufficient.

Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.

Statement 1 tells us that the volume of the cube is , from this we can find the length of the side of the cube. Statement 1 alone is sufficient.

Statement 2, tells us that the area of ABCD is , similarily, by taking the square root of this number, we can find the length of the edge of the cube.

Therefore each statement alone is sufficient.

Statement 1: Use the volume formula for a cube to solve for the side length.

where represents the length of the edge

Statement 2: Use the surface area formula for a cube to solve for the side length.

Each statement alone is sufficient to answer the question.

Call the sidelength, surface area, and volume of the cube , , and , respectively.

Then

or, equivalently,

So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be

Also,

or, equivalently,

Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be

Therefore, the answer is that either statement alone is sufficient.

The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula can be used to find the volume of the sphere.

In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.

Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is where is the length of an edge of the cube and is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.

Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.

Statement 1 alone is sufficient.

Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.

Statement 1 tells us that the volume of the cube is , from this we can find the length of the side of the cube. Statement 1 alone is sufficient.

Statement 2, tells us that the area of ABCD is , similarily, by taking the square root of this number, we can find the length of the edge of the cube.

Therefore each statement alone is sufficient.

Statement 1: Use the volume formula for a cube to solve for the side length.

where represents the length of the edge

Statement 2: Use the surface area formula for a cube to solve for the side length.

Each statement alone is sufficient to answer the question.

Call the sidelength, surface area, and volume of the cube , , and , respectively.

Then

or, equivalently,

So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be

Also,

or, equivalently,

Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be

Therefore, the answer is that either statement alone is sufficient.

The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula can be used to find the volume of the sphere.

In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.

Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is where is the length of an edge of the cube and is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.

Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.

Statement 1 alone is sufficient.

Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.

Statement 1 tells us that the volume of the cube is , from this we can find the length of the side of the cube. Statement 1 alone is sufficient.

Statement 2, tells us that the area of ABCD is , similarily, by taking the square root of this number, we can find the length of the edge of the cube.

Therefore each statement alone is sufficient.

Statement 1: Use the volume formula for a cube to solve for the side length.

where represents the length of the edge

Statement 2: Use the surface area formula for a cube to solve for the side length.

Each statement alone is sufficient to answer the question.

Call the sidelength, surface area, and volume of the cube , , and , respectively.

Then

or, equivalently,

So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be

Also,

or, equivalently,

Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be

Therefore, the answer is that either statement alone is sufficient.

The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula can be used to find the volume of the sphere.

In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.

Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is where is the length of an edge of the cube and is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.

Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.

Statement 1 alone is sufficient.

Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.

Statement 1 tells us that the volume of the cube is , from this we can find the length of the side of the cube. Statement 1 alone is sufficient.

Statement 2, tells us that the area of ABCD is , similarily, by taking the square root of this number, we can find the length of the edge of the cube.

Therefore each statement alone is sufficient.

Statement 1: Use the volume formula for a cube to solve for the side length.

where represents the length of the edge

Statement 2: Use the surface area formula for a cube to solve for the side length.

Each statement alone is sufficient to answer the question.