Pythagorean Theorem

Question

hello!

 

A diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube. Find the length of a diagonal d in a cube that has an edge of length 10 meters.

 

I've got an answer... But I'm not so sure about it. I got 17.3 and I have a feeling that it's wrong. I need help.

 

thank you in advance!

Answer 1

The diagonal on one face is given by X^2 = 10^2 + 10^2

 

The above face diagonal now forms a side along with the edge for the body diagonal

 

This final diagonal d^2 is given by;

 

d^2 = a^2 + 10^2

 

but as shown above a^2 is 10^2 + 10^2

 

Hence d^2 = 10^2 + 10^2 + 10^2

 

therefore d = (10^2 + 10^2 + 10^2)^1/2

 

d = 10(3)^1/2 = 17.32 meters

Answer 2

Think about the cube.  The diagonal described goes from "one of the cube's top corners to the opposite corner of the base of the cube."

 

This diagonal is the hypotenuse of a right triangle.  One side of that triangle is an edge of the cube (length=10 meters).  The other side of that right triangle is the diagonal of the base,

 

So, you must use the Pythagorean Theorem twice:  once to find the diagonal across the base; once to find the diagonal that goes through the cube.

 

   10² + 10² = d₁²

    14.14 = d₁                    [diagonal across the base]

 

   10²  + 14.14² = d₂²

    100 + 200 = d₂²

         17.3 = d₂            [diagonal through the cube]

 

Now, feeling right when you are right or feeling wrong when you are wrong are both expected.  But, you may be wrong and feel you are right (Type I error -- you loose points) or you may be right and feel you are wrong (Type II error -- you still get the points).  So, find ways to verify the processes you used (not just the answer) and you will gain confidence in the answer !