SOLUTION: Please help! Geometry: A cube has sides of lenght [5] find the area of one side of cube, find the volume of the cube, find the lenght if the diagonal of one of the sides, find teh

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Question 487782: Please help!
Geometry: A cube has sides of lenght [5] find the area of one side of cube, find the volume of the cube, find the lenght if the diagonal of one of the sides, find teh distance from A to B on a cube
I need deatiled answers please I need ASAP
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the measure of an edge of a cube. Then the area of one side of the cube is , the volume of the cube is , the diagonal of a side is , and the diagonal of the cube is .

The formula for the diagonal of a side is from Pythagoras:



The formula for the diagonal of the cube is also from Pythagoras:



John

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Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Detailed explanation:

Let's find the diagonal AC of the bottom square, drawn in green below:



Triangle ADC is a right triangle, with right angle ADC so we use the
Pythagorean theorem:

AC² = AD² + DC² 
AC² = 5² + 5²
AC² = 25 + 25
AC² = 50
       __    ____    __  _     _ 
 AC = Ö50 = Ö25×2 = Ö25×Ö2 = 5Ö2
                                                            _
That's the first answer.  So we label that green diagonal 5Ö2



Let's draw the cube's diagonal AB in green also




Triangle ABC is a right triangle with right angle ACB. So we use
the Pythagorean theorem to find AB

AB² = AC² + BC²
         _
AB² = (5Ö2)² + 5²
          _
AB² = 5²(Ö2)² + 25

AB² = 25(2) + 25

AB² = 50 + 25

AB² = 75
       __    ____    __  _     _
 AB = Ö75 = Ö25×3 = Ö25×Ö3 = 5Ö3

Edwin