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Given that the volume that a cube is

*
, what is the size of any type of one of its sides?

 


*


*


*


*


Explanation:

*

The formula because that the volume is given by

*

Since we have actually the volume, we need to take the cube root of the volume to find the size of any one side (since it is a cube, all of the sides room equal).

You are watching: How to find the edge length of a cube with volume

 

*

Plugging in 216 for the volume, we end up with

*


A challenge of a cube has a diagonal through a size of

*
. What is the length of one of the edges of the cube?

 

*


Explanation:

Because this is a cube, it"s helpful to remember the the value of the diagonal of one face is the same size for the other 5 faces. Additionally, the size of one edge will be the same size of all the cube"s other edges. This helps relax the stress of there being much more than one possible right answer. 

To discover the edge, we"re searching for the size of among the political parties of the square"s faces. The problem can be seen in a simplified square convention: 

*

*

The hypotenuse that the produced triangle is

*
, which can be set equal to
*
 to deal with for
*
, which in this case will give us the length of one of the cube"s edges. 

*

*

*

Therefore, the edge length of the cube is 

*
.


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Example question #3 : exactly how To discover The size Of An sheet Of A Cube


If the surface area that a cube is same to 

*
, what is the size of one of the cube"s sides?


Possible Answers:
Correct answer:

*


Explanation:

The surface ar area the a cube have the right to be stood for as 

*
, due to the fact that a cube has actually six sides and also the surface ar area of each side is represented by its length multiplied by its width, which because that a cube is 
*
, since every one of its edges are the very same length.

We deserve to substitute

*
 into this equation and also then settle for 
*
:

*

*

*

*

So, one edge that this cube is 

*
 in length.


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Example inquiry #1 : how To discover The length Of An leaf Of A Cube


The volume the a cube is

*
.


Find the length of the cube come the nearest tenth the a foot.


Possible Answers:
Correct answer:

*


Explanation:

Since the volume that a cube is length times broad times height, v every measurement gift the same, we just need to take it the cube root of the volume:

 

*
.

Rounded come the nearest tenth, the size is 3.5 feet.


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Example question #5 : how To discover The length Of An edge Of A Cube


Find the length of one of the cube"s sides:

*


Possible Answers:

Cannot it is in determined 


Correct answer:

*


Explanation:

The only info that is provided is the the diagonal of one of the encounters of the cube is

*
. Since this is a cube, this is true for the rest of the five faces. All the edges will likewise be the exact same length, definition this eliminates the possibility of more than one correct answer.

The leaf of the cube have the right to be fixed for using the Pythagorean Theorem due to the fact that the diagonal create two ideal triangles. Or, if you"re comfortable v it, you can remember that the diagonal line creates 2

*
 special best triangles that have actually their own rules v respect to addressing for sides.

Using the Pythagorean Theorem, 

*
, we have the right to simplify the equation follow to information we have and also can deduce the correct answer.

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The variables

*
 and
*
 refer to the legs of the appropriate triangles. Since this is a cube, we have the right to deduce that the size of the legs will be the same. Therefore,
*
. That means the Pythagorean to organize (for this case) deserve to be rewritten as 
*

Looking back at the problem, the only information given is the hypotenuse for one of the 2 triangles. This value can be substituted in for

*
. Then, together we settle for
*
, us will attain the answer for the question: the size of the edge.