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

Answer: 144 cm^2

Question 2: Find the volume of a pyramid with a rectangular base measuring 8 cm by 10 cm and a height of 12 cm.

Answer: 960 cm^3

Question 3: A pyramid has a base perimeter of 20 cm and a slant height of 7 cm. If the base is a regular pentagon, what is the approximate surface area? (Use  = 3.14 for .)

Answer: Approx. 135.8 cm^2

Question 4: Construct a pyramid with a triangular base measuring 5 cm on each side and a height of 8 cm. Show all steps in your drawing.

Answer: Constructed pyramid with proper dimensions and labels.

Question 5: Determine the lateral surface area of a regular square-based pyramid with base side length 10 cm and a slant height of 13 cm.

Answer: 260 cm^2

Question 6: A pyramid has a height of 15 cm and a base area of 36 cm^2. Calculate its volume.

Answer: 180 cm^3

Question 7: A student mistakenly uses  = 3.14 to calculate the surface area of a pyramid and gets an incorrect result. Identify a common mistake made in such calculations and explain how to correct it.

Answer: Mistake: Using  as a distance instead of circumference. Correction: Use the correct formula for lateral face area and surface area, ensuring  is the value of , not circumference.

Question 8: A square pyramid and a triangular pyramid have the same volume of 120 cm^3. The square pyramid has a base side of 6 cm, find the height. The triangular pyramid has a base of 8 cm and height 5 cm; determine its height.

Answer: Square pyramid height: 8.33 cm; Triangular pyramid height: 15 cm

Question 9: Plot the graph of y=  x for x from -5 to 5 on the grid.

Answer: Graph of y=3.14x from x=-5 to 5

Question 10: Construct a pyramid with a square base of side 4 cm and a slant height of 6 cm. Label all parts clearly.

Answer: Constructed pyramid with all dimensions and labels.

Question 11: A pyramid has a base area of 50 cm^2 and a height of 10 cm. Calculate its volume.

Answer: 500 cm^3

Question 12: Explain why the slant height of a pyramid is important for calculating surface area. Provide an example of how an incorrect slant height affects the calculation.

Answer: Slant height determines the area of the lateral faces; an incorrect value leads to wrong surface area. For example, underestimating it results in a smaller calculated surface area.