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Find the length of the diagonal of a cube through side size of 

*
.

You are watching: Length of a diagonal of a cube


*


*


*


*


Explanation:

We start with a picture, noting that the diagonal, labeled as 

*
, is the length throughout the cube native one vertex come the the contrary side"s vertex.

*

However, the cheat to solving the trouble is to additionally draw in the diagonal line of the bottom confront of the cube, which we labeled 

*
.

*

Note that this create two appropriate triangles. Despite our finish goal is to find 

*
, us can begin by looking at the ideal triangle in the bottom face to find 
*

*

Now the we understand the value of 

*
, we have the right to turn to our 2nd right triangle to find 
*
 using the Pythagorean Theorem.

*

*

*

Taking the square source of both sides and simplifying provides the answer.

*


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Example question #2 : how To uncover The diagonal Of A Cube


What is the diagonal length for a cube v volume of 

*
 
*
? round to the nearest hundredth.


Possible Answers:
Correct answer:

*
 
*


Explanation:

Recall the the volume the a cube is computed utilizing the equation

*
, where 
*
 is the length of one next of the cube.

So, because that our data, we know:

*

Using her calculator, take the cube source of both sides. Girlfriend can always do this by raising 

*
 to the 
*
 power if her calculator does not have actually a varied-root button.

*

If girlfriend get 

*
, the worth really must be rounded increase to 
*
. This is because of calculator estimations. So, if the political parties are 
*
 
*
, you can find the diagonal line by using a sport on the Pythagorean Theorem functioning for three dimensions:

*

*

This is 

*
. Round it to 
*
.


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Example inquiry #3 : just how To discover The diagonal line Of A Cube


What is the size of the diagonal of a cube with a volume of 

*
?


Possible Answers:
Correct answer:

*


Explanation:

Recall that the diagonal line of a cube is most easily discovered when you recognize that cube"s dimensions. For the volume the a cube, the pertinent equation is:

*
, where 
*
 represents the length of one next of the cube. For our data, this gives us:

*

Now, you might factor this by hand or usage your calculator. You will check out that 

*
 is 
*
.

Now, we uncover the diagonal line by using a three-dimensional variation of the Pythagorean organize / distance formula:

*
 or 
*

You can rewrite this:

*


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