Calculating Pyramid Height with the Pythagorean Theorem

The video tutorial explains how to calculate the volume of a pyramid when given the base dimensions and the slant height but not the vertical height. It demonstrates using the Pythagorean theorem to find the height of the pyramid and then applies the volume formula to compute the final volume. The tutorial emphasizes the importance of correctly identifying and using the hypotenuse and other triangle sides in calculations.

What are the given dimensions for the base of the pyramid?

• Length 9 meters, Width 9 meters

• Length 10 meters, Width 10 meters

• Length 8 meters, Width 9 meters

• Length 9 meters, Width 8 meters

What crucial measurement is missing for calculating the pyramid's volume?

• Height of the pyramid

• Slant height of the pyramid

• Volume of the pyramid

• Area of the base

Which theorem is used to calculate the height of the pyramid?

• Euclid's theorem

• Fermat's Last Theorem

• Pythagorean theorem

• Thales' theorem

What is the length of the hypotenuse used in the calculation?

• 4.5 meters

• 9 meters

• 24.6 meters

• 25 meters

How is the distance from the center of the pyramid's base to the side calculated?

• Base length divided by 2

• Height of the pyramid divided by 2

• Base width divided by 2

• Slant height divided by 2

What is the distance from the center to the side of the pyramid's base?

• 25 meters

• 24.6 meters

• 9 meters

• 4.5 meters

What is the calculated height of the pyramid?

• 25 meters

• 9 meters

• 24.6 meters

• 4.5 meters

What formula is used to calculate the volume of the pyramid?

• (Length x Width) / Height

• (Length + Width + Height) / 3

• (Length x Width x Height) / 3

• Length x Width x Height

What is the final volume of the pyramid in cubic meters?

• 700 cubic meters

• 600 cubic meters

• 650 cubic meters

• 664.2 cubic meters

What mistake was corrected regarding the unit of the pyramid's volume?

• From square yards to cubic meters

• From liters to cubic meters

• From cubic yards to cubic meters

• From square meters to cubic meters