How to find the length of an edge of a cube - GRE Quantitative Reasoning
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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 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?
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 just 
times 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.
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 just
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.
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What is the length of an edge of a cube with a surface area of 
?
What is the length of an edge of a cube with a surface area of
The surface area of a cube is made up of 
squares. Therefore, the equation is merely 
times the area of one of those squares. Since the sides of a square are equal, this is:
, where 
is 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
The surface area of a cube is made up of
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
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If a cube has a total surface area of 
square inches, what is the length of one edge?
If a cube has a total surface area of
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.
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.
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