Pythagorean Theorem in 3D Shapes

The video tutorial explains the application of Pythagoras theorem in 3D geometry, focusing on finding the diagonal lengths in a cuboid and a square base pyramid. It demonstrates step-by-step calculations using the theorem to solve for unknown lengths, emphasizing the importance of not rounding intermediate results until the final answer is reached.

What are the dimensions of the cuboid used in the 3D Pythagoras example?

• 15 cm width, 20 cm length, 10 cm height

• 10 cm width, 15 cm length, 20 cm height

• 20 cm width, 10 cm length, 15 cm height

• 15 cm width, 10 cm length, 20 cm height

Which theorem is used to find the diagonal on the base of the cuboid?

• Fermat's Last Theorem

• Euclid's theorem

• Thales' theorem

• Pythagorean theorem

What is the length of the diagonal on the base of the cuboid?

• 20 cm

• 25 cm

• 15 cm

• 30 cm

How is the diagonal through the cuboid calculated?

• Using the base diagonal and the width

• Using the width and the height

• Using the length and the height

• Using the base diagonal and the height

What is the approximate length of the diagonal through the cuboid?

• 25.0 cm

• 28.5 cm

• 30.0 cm

• 26.9 cm

In the pyramid problem, what is the first step to find the diagonal from the base to the apex?

• Find the length of one side of the base

• Find the diagonal across the base

• Find the height of the pyramid

• Find the volume of the pyramid

What shape is the base of the pyramid in the problem?

• Circle

• Square

• Triangle

• Rectangle

What is the length of the diagonal across the base of the pyramid?

• 11.31 cm

• 12.00 cm

• 10.00 cm

• 13.50 cm

What is the final length of the diagonal from the base to the apex of the pyramid?

• 16 cm

• 12 cm

• 10 cm

• 14 cm

Which theorem is repeatedly used to solve both the cuboid and pyramid problems?

• Pythagorean theorem

• Fundamental theorem of calculus

• Binomial theorem

• Remainder theorem