Understanding Cube Diagonals and Volume

The video tutorial explains how to find the volume of a cube given its diagonal length. It uses the 45-45-90 triangle rule to determine the side length of the cube. The diagonal of the cube is 6 units, and the tutorial demonstrates how to calculate the side length by dividing the hypotenuse by the square root of 2. The process of rationalizing the expression is shown, resulting in a side length of 3√2. Finally, the video calculates the volume by cubing the side length, resulting in a volume of 54√2 cubic units.

What is the length of the diagonal of the cube mentioned in the problem?

• 6 units

• 7 units

• 5 units

• 4 units

Which geometric rule is used to find the side length of the cube?

• 30-60-90 triangle rule

• Pythagorean theorem

• 60-60-60 triangle rule

• 45-45-90 triangle rule

How do you calculate the side length of the cube using the diagonal?

• Subtract the square root of 2 from the diagonal

• Multiply the diagonal by 2

• Divide the diagonal by the square root of 2

• Add the diagonal to the square root of 2

What is the side length of the cube after applying the 45-45-90 rule?

• 6 square root 2 units

• 3 units

• 3 square root 2 units

• 6 units

What is the final volume of the cube?

• 27 square root units cubed

• 54 units cubed

• 54 square root units cubed

• 27 units cubed