Question 1: A square pyramid has a base edge of 6 cm and a slant height of 8 cm. Calculate its lateral surface area.

Answer: 96 cm^2

Question 2: Calculate the volume of a pyramid with a base area of 50 cm^2 and a height of 12 cm.

Answer: 200 cm^3

Question 3: Construct a triangular pyramid with a base side of 4 cm, height of 3 cm, and a lateral face slant height of 5 cm. Draw the net on the grid.

Answer: Net drawing on grid

Question 4: A pyramid has a square base with side length 10 cm. Its slant height is 13 cm. Find the total surface area.

Answer: 290 cm^2

Question 5: Explain why the volume formula for a pyramid is  imes Base Area imes Height, and why it is different from the volume of a prism.

Answer: Because pyramids taper to a point, their volume is one-third that of a prism with the same base and height.

Question 6: A hexagonal pyramid has a base edge of 4 cm and a height of 9 cm. Calculate its lateral surface area, assuming each lateral face is an equilateral triangle.

Answer: 48√3 cm^2

Question 7: A real-world scenario: A monument is designed as a square pyramid with a base of 15 meters and a height of 10 meters. If the architect wants to estimate the amount of materials needed for the outer surface, which surface area calculation should be used and why?

Answer: Lateral surface area for outer shell; total surface area if covering the entire outside.

Question 8: A pyramid has a base with side length 8 cm and a height of 6 cm. Find the volume, showing all steps.

Answer: 128 cm^3

Question 9: Identify and correct the common mistake: A student calculates the surface area of a pyramid by adding all the edges. Is this correct? Explain your answer.

Answer: No, surface area is the total outer area of all faces, not edges.

Question 10: A triangular pyramid has a base of 5 cm sides, and each lateral face has a slant height of 7 cm. Calculate the total surface area.

Answer: 70.83 cm^2

Question 11: Challenge: Derive the formula for the volume of a pyramid starting from the volume of a prism, explaining each step.

Answer: The volume of a pyramid is one-third that of a prism with the same base and height because of the way the space is shared, which can be shown through calculus or geometric slicing.