DSQ: Calculating the length of an edge of a cube - GMAT Quantitative Reasoning
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What is the length of the edge of a cube?
-
Its volume is 1,728 cubic meters.
-
Its surface area is 864 square meters
What is the length of the edge of a cube?
-
Its volume is 1,728 cubic meters.
-
Its surface area is 864 square meters
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.
Call the sidelength, surface area, and volume of the cube
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.
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A sphere is inscribed inside a cube. What is the volume of the sphere?
Statement 1: The surface area of the cube is 216.
Statement 2: The volume of the cube is 216.
A sphere is inscribed inside a cube. What is the volume of the sphere?
Statement 1: The surface area of the cube is 216.
Statement 2: The volume of the cube is 216.
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.
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
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What is the length of edge 
of cube 
?
(1) 
.
(2) 
.
What is the length of edge
(1)
(2)
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.
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
Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.
Statement 1 alone is sufficient.
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is a cube. What is the length of edge 
?
(1) The volume of the cube is 
.
(2) The area of face 
is 
.
(1) The volume of the cube is
(2) The area of face
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.
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
Statement 2, tells us that the area of ABCD is
Therefore each statement alone is sufficient.
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Find the length of an edge of the cube.
- The volume of the cube is
.
- The surface area of the cube is
.
Find the length of an edge of the cube.
- The volume of the cube is
- The surface area of the cube is
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.
Statement 1: Use the volume formula for a cube to solve for the side length.
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.
Compare your answer with the correct one above