GMAT Math : Cubes
Study concepts, example questions & explanations for GMAT Math
All GMAT Math Resources
Example Questions
Example Question #51 : Rectangular Solids & Cylinders
What is the length of the edge of a cube?
1) Its volume is 1,728 cubic meters.
2) Its surface area is 864 square meters
EACH statement ALONE is sufficient.
Statements 1 and 2 TOGETHER are not sufficient.
Statement 1 ALONE is sufficient, but Statement 2 alone is not sufficient.
BOTH statements TOGETHER are sufficient, but neither statement ALONE is sufficient.
Statement 2 ALONE is sufficient, but Statement 1 alone is not sufficient.
EACH 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.
Example Question #52 : Rectangular Solids & Cylinders
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.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
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 
Example Question #53 : Rectangular Solids & Cylinders
What is the length of edge 
(1) 
(2) 
Each statement alone is sufficient.
Statements 1 and 2 together are not sufficient.
Statement 2 alone is sufficient.
Statement 1 alone is sufficient.
Both statements together are sufficient.
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.
Example Question #54 : Rectangular Solids & Cylinders
(1) The volume of the cube is 
(2) The area of face 
Both statements together are sufficient.
Statement 1 alone is sufficient.
Each statement alone is sufficient.
Statements 1 and 2 together are not sufficient.
Statement 2 alone is sufficient.
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.
Example Question #337 : Data Sufficiency Questions
Find the length of an edge of the cube.
- The volume of the cube is
.
- The surface area of the cube is
.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
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.
Example Question #4 : Cubes
(1) The area of a face of the cube is 
(2) The length of 
Both statements taken together are sufficient.
Each statement alone is sufficient.
Statement 2 alone is sufficient.
Statement 1 alone is sufficient.
Statements 1 and 2 taken together are not sufficient.
Each statement alone is sufficient.
To know the diagonal HB of the cube, we need to have information about the length of the edges of the cube. Knowing the area of a face would allow us to find the length of an edge; therefore statement 1 alone is sufficient.
Statment 2 alone is sufficient as well since the length of a diagonal of a square is given by 
Therefore each statement alone is sufficient.
Example Question #5 : Cubes
Calculate the diagonal of a cube.
- The surface area of the cube is
.
- The volume of the cube is
.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Statement 1: We can use the surface area to find the length of the cube's edge and then determine the length of the diagonal.
where 
Now that we know the length of the edge, we can find the length of the diagonal: 
Statement 2: Once again, we can use the provided information to find the length of the cube's edge.
Which means the length of the diagonal is 
Thus, each statement alone is sufficient to answer the question.
Example Question #341 : Data Sufficiency Questions
Give the length of the diagonal of the cube.
- The surface area of the cube is
.
- The volume of the cube is
.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Statement 1: To find the length of the diagonal of the cube we need to find the length of the cube's edge. We can use the given surface area value to do so:
Now that we know the length of the cube's edge, we can calculate the diagonal:
Statement 2: We're given the volume of the cube which we can also use to solve for the length of the cube's edge.
Knowing the length of the cube's edge allows us to calculate the diagonal:
Each statement alone is sufficient to answer the question.
Example Question #342 : Data Sufficiency Questions
Find the diagonal of the cube.
- The surface area of the cube is
.
- The length of an edge of the cube measures
.
Each statement alone is sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Statement 1: We need the length of an edge in order to find the diagonal of the cube. Luckily, we can find the length using the information provided:
Now that we know the length of an edge is 11 cm we can find the length of the diagonal.
Statement 2: We're given the information we need to find the diagonal, all we need to do is plug it into the equation
Example Question #61 : Rectangular Solids & Cylinders
What is the length of the diagonal of the cube A if the diagonal of cube B is 
- The lengths of the edges of cube A to cube B is a ratio of 1:2.
- The surface area of cube A is
.
Each statement alone is sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Statement 1: The information provided in the question is only useful if we're given a relationship between cube A and cube B. Since this statement does provide us with the ratio of 1:2, we can answer the question.
where 
we can easily see the length measures
Remember the ratio of cube A to cube B is 1:2.
Now that we know the length, we can find the diagonal of the cube:
Statement 2: We're given information about cube A so we don't need to worry about cube B. Using this information we can solve for the edge length of cube A and then calculate the diagonal.
Knowing the length of the edge allows us to find the diagonal of the cube
All GMAT Math Resources
