Question 1: Calculate the volume of a pyramid with a square base of side length 6 cm and a height of 9 cm.

Answer: 108

Question 2: A rectangular pyramid has a base area of 24 cm² and a height of 10 cm. What is its volume?

Answer: 80

Question 3: Construct a triangular pyramid with a base area of 12 cm² and a height of 8 cm. Calculate its volume.

Answer: 32

Question 4: A pyramid has a base area of 15 cm² and a height of 12 cm. What is its volume? Show your working.

Answer: 60

Question 5: Identify the common mistake in calculating the volume of a pyramid if someone uses Base Area × Height instead of ⅓ × Base Area × Height. Explain why this is incorrect.

Answer: They overestimate the volume by a factor of 3; the correct volume is one-third of Base Area times Height.

Question 6: A student calculates the volume of a pyramid as 50 cm³, given a base area of 25 cm² and height of 4 cm. Identify and correct the mistake.

Answer: The student used Base Area × Height instead of ⅓ × Base Area × Height. Correct volume = (1/3) × 25 × 4 = 33.33 cm³.

Question 7: Plot the graph of y = 2x for x values from 0 to 5 on the provided grid. What is the value of y when x=3?

Answer: 6

Question 8: Construct a pyramid with a rectangular base measuring 8 cm by 10 cm and a height of 15 cm. Calculate its volume.

Answer: 400

Question 9: A pyramid’s base has an area of 18 cm², and its height is 7 cm. A student mistakenly multiplies base area by height to find volume. What is the correct volume? Show your working.

Answer: Correct volume = (1/3) × 18 × 7 = 42 cm³

Question 10: Challenge: A pyramid has a square base with side length 10 cm and a slant height of 13 cm. If the height is unknown, but the slant height and base are given, explain how to find the height and then the volume.

Answer: Use the Pythagorean theorem: height = √(13² - 5²) = √(169 - 25) = √144 = 12 cm. Then volume = (1/3) × 100 × 12 = 400 cm³.