Question 1: Calculate the volume of a cone with radius 4 cm and height 9 cm. Use ⅓πr²h as the formula.

Answer: 150.8

Question 2: A cone has radius 3 m and height 12 m. Find its volume. Show your working.

Answer: 101.8

Question 3: If the volume of a cone is 125π cm³ and the height is 10 cm, what is the radius?

Answer: 5

Question 4: Construct a cone with radius 2 cm and height 8 cm on the grid. Then, calculate its volume.

Answer: 33.51

Question 5: A cone has radius 5 cm and height 15 cm. What is its volume? Round to two decimal places.

Answer: 392.70

Question 6: A cone has a volume of 200π cm³ and radius 6 cm. Find its height.

Answer: 7.02

Question 7: A real-world scenario: A funnel in a science experiment has a cone shape with radius 3 inches and height 6 inches. How much liquid, in cubic inches, can it hold?

Answer: 16.76

Question 8: Identify the common mistake: A student calculates the volume of a cone with radius 4 cm and height 10 cm as 80π cm³ using the formula ⅓πr²h. What is the mistake?

Answer: Incorrect application of formula or missing ⅓ factor

Question 9: A cone with radius 7 cm has a volume of 462π cm³. Find its height.

Answer: 6

Question 10: Challenge: Derive the formula for the volume of a cone starting from the volume of a cylinder, explaining each step.

Answer: Students should explain that a cone is a pyramid with a circular base and relate the volume of a cone to that of a cylinder with the same base and height, resulting in ⅓πr²h.