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Given that the volume the a cube is

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

 


*


*


*


*


Explanation:

*

The formula for the volume is given by

*

Since we have actually the volume, we have to take the cube source of the volume to find the length of any kind of one side (since it is a cube, every one of the sides room equal).

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*

Plugging in 216 because that the volume, we end up with

*


A face of a cube has actually a diagonal through a length of

*
. What is the size of one of the edge of the cube?

 

*


Explanation:

Because this is a cube, it"s beneficial to remember that the worth of the diagonal of one challenge is the same length for the other five faces. Additionally, the size of one edge will certainly be the same length of all the cube"s other edges. This helps relieve the stress of there being an ext than one feasible right answer. 

To discover the edge, we"re searching for the length of among the sides of the square"s faces. The trouble can be viewed in a streamlined square convention: 

*

*

The hypotenuse of the produced triangle is

*
, which deserve to be set equal come
*
 to settle for
*
, which in this instance will offer us the length of one of the cube"s edges. 

*

*

*

Therefore, the edge length of the cube is 

*
.


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Example inquiry #3 : Cubes


If the surface area of a cube is same to 

*
, what is the size of among 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 every side is represented by its size multiplied through its width, which because that a cube is 
*
, since every one of its edges are the exact same length.

We deserve to substitute

*
 into this equation and also then resolve for 
*
:

*

*

*

*

So, one edge of this cube is 

*
 in length.


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Example concern #4 : Cubes


The volume that a cube is

*
.


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


Possible Answers:
Correct answer:

*


Explanation:

Since the volume that a cube is size times broad times height, through every measurement gift the same, we just need to take the cube source of the volume:

 

*
.

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


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Example inquiry #5 : Cubes


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

*


Possible Answers:

Cannot it is in determined 


Correct answer:

*


Explanation:

The only details that is provided is the the diagonal of among the deals with of the cube is

*
. Due to the fact that this is a cube, this is true for the remainder of the five faces. All the edge will also be the exact same length, an interpretation this eliminates the opportunity of an ext than one exactly answer.

The edge of the cube deserve to be fixed for using the Pythagorean Theorem since the diagonal create two best triangles. Or, if you"re comfortable with it, you deserve to remember that the diagonal line creates 2

*
 special right triangles that have their very own rules v respect to addressing for sides.

Using the Pythagorean Theorem, 

*
, we can simplify the equation according to info we have and also can deduce the exactly answer.

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The variables

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

Looking earlier at the problem, the just information provided is the hypotenuse for among the 2 triangles. This value deserve to be substituted in because that

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