All GMAT Math Resources
Example Questions
Example Question #1 : Cubes
If the volume of a cube is units cubed, what is the length of each side of the cube?
We solve for the side of the cube by deriving it from the volume of a cube formula:
Example Question #2 : Cubes
If a cube has a surface area of , what is the length of one side?
To find the surface area of a cube, use the following formula:
Where s is our side length.
Rearrange for s to get the following:
Plug in 54 for SA and solve
Don't forget your units, in this case centimeters so we get 3 centimeters
Example Question #3 : Calculating The Length Of An Edge Of A Cube
If a cube has a surface area of , what is the length of one of its sides?
To solve for the side length of the cube, we need to use the formula for surface area. There are six faces on a cube, so its total surface area is just six times the area of one of its square faces, which is given by the side length squared:
Example Question #4 : Calculating The Length Of An Edge Of A Cube
If a cube has a volume of and is made up of smaller cubes, what is the length of one side of one of the smaller cubes?
Volume of a cube is equal to the cube of its side. 343 is equal to 7 cubed, so the length of the whole cube is 7 cm. The cube is made up of 27 smaller cubes though. That means that one face of the cube is made up of 9 cubes and one edge of the whole cube is made up of 3 small cubes. That means that the length of one small cube is equal to the total length of one side divided by the numbers of cubes per side
Then we get our final answer by doing:
Example Question #5 : Calculating The Length Of An Edge Of A Cube
is a cube with diagonal . What is the length of an edge of the cube?
We are given the length of the diagonal of the cube.
Therefore we can find the length of an edge by using the formula
or , and .
Therefore, the final answer is .
Example Question #3 : Cubes
Find the length of the edge of a cube given that the volume is .
To find side length, you must use the equation for volume of a cube and solve for .
Thus,
Example Question #4 : Cubes
What is the length of the diagonal of a cube if its side length is ?
The diagonal of a cube extends from one of its corners diagonally through the cube to the opposite corner, so it can be thought of as the hypotenuse of a right triangle formed by the height of the cube and the diagonal of its base. First we must find the diagonal of the base, which will be the same as the diagonal of any face of the cube, by applying the Pythagorean theorem:
Now that we know the length of the diagonal of any face on the cube, we can use the Pythagorean theorem again with this length and the height of the cube, whose hypotenuse is the length of the diagonal for the cube:
Example Question #5 : Cubes
is a cube and face has an area of . What is the length of diagonal of the cube ?
To find the diagonal of a cube we can apply the formula , where is the length of the diagonal and where is the length of an edge of the cube.
Since we are given an area of a face of the cube, we can find the length of an edge simply by taking its square root.
Here the length of an edge is 3.
Thefore the final andwer is .
Example Question #571 : Geometry
What is the length of the diagonal of cube , knowing that face has diagonal equal to ?
To find the length of the diagonal of the cube, we can apply the formula, however, we firstly need to find the length of an edge, by applying the formula for the diagonal of the square.
where is the diagonal of face ABCD, and , the length of one of the side of this square.
The length of must be , which is the length of the edges of the square.
Therefore we can now use the formula for the length of the diagonal of the cube:
, where is the length of an edge.
Since , we get the final answer .
Example Question #5 : Cubes
A given cube has an edge length of . What is the length of the diagonal of the cube?
Not enough information provided
The diagonal of a cube with an edge length can be defined by the equation . Given in this instance, .