Question 1: Calculate the surface area of a square-based pyramid with a base side of 6 cm and a slant height of 10 cm.

Answer: 192

Question 2: Find the volume of a pyramid with a square base of side 4 cm and height 9 cm.

Answer: 48

Question 3: A pyramid has a rectangular base measuring 8 cm by 5 cm. The vertical height from the base to the apex is 12 cm. Calculate its volume.

Answer: 240

Question 4: Construct a triangular pyramid with equilateral triangular bases each side measuring 6 cm and a height of 8 cm.

Answer: Students will draw on grid

Question 5: Explain why a pyramid with a triangular base is classified as a square pyramid.

Answer: It is not classified as a square pyramid; a square pyramid has a square base. If a pyramid has a triangular base, it is a triangular pyramid or tetrahedron.

Question 6: A pyramid with a base edge of 10 cm and a slant height of 13 cm has a height of 9 cm. Calculate its total surface area.

Answer: 290

Question 7: Using the formula for volume, compare the volumes of two pyramids: one with a base area of 36 cm² and height 8 cm, and another with base area 48 cm² and height 6 cm. Which has a larger volume?

Answer: First pyramid, volume= (1/3)*36*8=96 cm³; second= (1/3)*48*6=96 cm³; both have the same volume.

Question 8: A square pyramid has a volume of 80 cm³ and a base side length of 4 cm. Find its height.

Answer: 10

Question 9: Identify the common mistake when calculating the surface area of a pyramid and explain how to correct it.

Answer: Common mistake: using only the base area. Correct approach: include lateral faces and slant heights.

Question 10: A pyramid's lateral surface area is 150 cm², and the base area is 50 cm². Calculate its total surface area.

Answer: 200

Question 11: Challenge: A pyramid's base is an octagon with each side measuring 4 cm. If the pyramid's height is 10 cm, estimate its volume, assuming the base area is approximately 85.3 cm².

Answer: Approximately 285.3 cm³