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Example Questions
Example Question #1511 :Gre Quantitative Reasoning
Quantity A: The length of a side of a cube with a volume of.
Quantity B: The length of a side of a cube with surface area of.
Which of the following is true?
Quantity B is larger.
The relationship between the two quantities cannot be determined.
The two quantities are equal
Quantity A is larger.
The two quantities are equal
Recall that the equation for the volume of a cube is:
Since the sides of a cube are merely squares, the surface area equation is justtimes the area of one of those squares:
So, for our two quantities:
Quantity A
Use your calculator to estimate this value (since you will not have a square root key). This is.
Quantity B
First divide by:
Therefore,
Therefore, the two quantities are equal.
Example Question #2 :How To Find The Length Of An Edge Of A Cube
What is the length of an edge of a cube with a surface area of?
The surface area of a cube is made up ofsquares. Therefore, the equation is merelytimes the area of one of those squares. Since the sides of a square are equal, this is:
, whereis the length of one side of the square.
For our data, we know:
This means that:
Now, while you will not have a calculator with a square root key, you do know that. (You can always use your calculator to test values like this.) Therefore, we know that. This is the length of one side
Example Question #3 :How To Find The Length Of An Edge Of A Cube
If a cube has a total surface area ofsquare inches, what is the length of one edge?
There is not enough information given.
There are 6 sides to a cube. If the total surface area is 54 square inches, then each face must have an area of 9 square inches.
Every face of a cube is a square, so if the area is 9 square inches, each edge must be 3 inches.