Understanding Diagonals in a Cube

The video tutorial explains how to find the diagonal of a cube in two steps. First, it demonstrates finding the diagonal of a cube's face using the Pythagorean theorem. Then, it uses this diagonal to calculate the cube's diagonal. The tutorial also provides a shortcut formula for quickly determining the diagonals of any cube based on its side length.

What is the first step in finding the diagonal of a cube?

• Identify the vertices of the cube

• Calculate the volume of the cube

• Measure the side of the cube

• Find the diagonal of a face of the cube

Which theorem is used to find the diagonal of a face of the cube?

• Remainder theorem

• Pythagorean theorem

• Binomial theorem

• Fundamental theorem of calculus

What is the length of the diagonal of a face if the side of the cube is 6?

• 12

• 6√2

• 12√2

• 6

What is the next step after finding the diagonal of a face?

• Use it to find the diagonal of the entire cube

• Calculate the area of the face

• Measure the height of the cube

• Find the perimeter of the face

What are the legs of the triangle used to find the cube's diagonal?

• 6 and 6√2

• 6 and 12

• 12 and 12√2

• 6√2 and 12

What is the length of the diagonal of the cube if the side is 6?

• 18

• 12√3

• 12

• 6√3

What is the shortcut formula for the diagonal of a face of a cube with side length s?

• s√3

• s√2

• 2s

• 3s

What is the shortcut formula for the diagonal of the entire cube with side length s?

• s√2

• 3s

• s√3

• 2s

What is the relationship between the side length and the diagonal of a face?

• The diagonal is the side length times √2

• The diagonal is the side length times √3

• The diagonal is twice the side length

• The diagonal is half the side length

What is the relationship between the side length and the diagonal of the cube?

• The diagonal is twice the side length

• The diagonal is half the side length

• The diagonal is the side length times √2

• The diagonal is the side length times √3