A cube is 5in. in exterior dimension. What is the diagonal distance across the interior?

Question

A cube measures 5 inches in each exterior dimension. 

What is the diagonal distance across the interior of the cube from lower, outer corner, to the upper far outside corner?

Answer 1

Another way to look at it is as follows:

 

The Pythagorean theorem may be extended to dimensions greater than 2 e.g., in 3 dimensions the formula for the diagonal of a rectangular prism is √(l²+w²+h²). In a cube l, w, h are all equal (length, width, and height). Therefore our problem can also be solved by computing

 

length of the diagonal of a cube with side 5in = √(5²+5²+5²)=√(75)= 5√3in

Answer 2

First find the diagonal of the bottom face.

Using the Pythagorean Theorem...

c²=5²+5²

c²=25+25

c²=50

c=√50

c=5√2

Now you have the measures of the two legs of the right triangle whose hypotenuse is the diagonal distance across the interior of the cube.

c²=5²+(5√2)²

c²=25+50

c²=75

c=√75

c=5√3 inches or 8.66 inches