Question 1: Calculate the volume of a square-based pyramid with a base length of 6 meters and a height of 9 meters.

Answer: 108 cubic meters

Question 2: Determine the slant height of a pyramid with a base side of 4 meters and a vertical height of 6 meters.

Answer: 

Question 3: Construct a square pyramid with a base side of 5 cm and a height of 8 cm. Calculate its surface area.

Answer: Approximately 145 square centimeters

Question 4: In an engineering project, a pyramid-shaped roof has a base length of 10 meters and a height of 4 meters. What is its volume?

Answer: 133.33 cubic meters

Question 5: A pyramid has a rectangular base measuring 8 meters by 6 meters and a vertical height of 5 meters. Calculate its surface area.

Answer: Approximately 188.4 square meters

Question 6: Explain why pyramids with a square base tend to be more stable in structural engineering compared to those with triangle bases.

Answer: Square bases provide better load distribution and stability due to their symmetry and larger surface contact.

Question 7: Calculate the lateral surface area of a pyramid with a base side of 7 meters and a slant height of 10 meters.

Answer: 147 square meters

Question 8: A pyramid’s volume is 150 cubic meters. If the base area is 50 square meters, what is its height?

Answer: 6 meters

Question 9: A student incorrectly calculates the surface area of a pyramid as 200 square centimeters. The actual surface area is 250 square centimeters. Identify a common mistake that could lead to this error.

Answer: Overlooking the slant height or miscalculating the lateral surface area component.

Question 10: Challenge: Derive the formula for the lateral surface area of a pyramid with a regular polygon base, and explain each component.

Answer: Lateral surface area = (Perimeter of base / 2)  (slant height). Each side’s area is (side length  slant height).