Question 1: Calculate the volume of a cone with radius 3 cm and height 9 cm using the formula ⅓πr²h.

Answer: 254.47

Question 2: A cone has a radius of 5 cm and a height of 12 cm. Calculate its volume, giving your answer in cubic centimeters.

Answer: 314.16

Question 3: Construct a cone on the grid with a radius of 4 units and a height of 10 units. Use appropriate drawing techniques.

Answer: Approximate drawing

Question 4: A cone's volume is 150π cm³, and its height is 10 cm. Find the radius of the cone.

Answer: 3 cm

Question 5: Calculate the volume of a cone with radius 2.5 cm and height 7 cm. Provide your answer in cubic centimeters.

Answer: 43.41

Question 6: A radius of a cone is doubled while height remains the same. How does the volume change? Explain your reasoning.

Answer: The volume increases four times because volume is proportional to r².

Question 7: A conical tank has a radius of 6 meters and a height of 15 meters. Calculate its volume. Use π ≈ 3.14.

Answer: 1696.46

Question 8: Identify and correct the mistake in the following calculation: A cone with radius 4 cm and height 8 cm has a volume of 213.6 cm³ when calculated as ⅓ × 3.14 × 4² × 8.

Answer: Incorrect calculation; the actual volume is 134.04 cm³.

Question 9: Suppose a cone has a radius of 7 cm and a volume of 539.82 cm³. Find its height.

Answer: 6 cm

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

Answer: Volume of cone = ⅓ × volume of cylinder = ⅓ × πr²h.

Question 11: Plot the graph of y = ⅓πr²h as r varies from 0 to 10 units, with h fixed at 8 units. Use the grid to sketch the shape.

Answer: Graph of y = (π/3) × r² × 8, plotting for r=0 to 10.