Cube Geometry and Diagonal Calculations

The video tutorial explains how to calculate the length of a hole drilled diagonally through a cube bead. The instructor visualizes the cube, identifies the longest diagonal, and applies the Pythagorean theorem to find the diagonal's length. The final calculation reveals that the length of the hole is the square root of 3 over 2 centimeters.

What is the length of each edge of the cube bead?

• 1/2 cm

• 1/4 cm

• 1 cm

• 2 cm

What is the longest diagonal in a cube?

• The diagonal of one face

• The diagonal from one corner to the opposite corner

• The diagonal of the base

• The diagonal of the top face

Which theorem is used to calculate the diagonal of the cube's base?

• Euclid's theorem

• Fermat's theorem

• Thales' theorem

• Pythagorean theorem

What is the length of the diagonal of the cube's base?

• 1 cm

• 1/2 cm

• 1/√2 cm

• √2 cm

What is the formula for the hypotenuse in a right triangle?

• a^2 * b^2 = c^2

• a^2 - b^2 = c^2

• a^2 / b^2 = c^2

• a^2 + b^2 = c^2

What is the length of the hole drilled through the cube?

• 1/2 cm

• √3/2 cm

• 1 cm

• √2 cm

What is the square root of 4?

• 1

• 2

• 3

• 4

What is the sum of 1/2 and 1/4?

• 1

• 3/4

• 1/4

• 1/2

What is the square root of 3/4?

• √3

• 1/2

• 3/2

• √3/2

What is the final step in calculating the length of the hole?

• Subtracting the sides

• Dividing the sides

• Multiplying the sides

• Taking the square root