Question 1: Write down the formula for calculating the volume of a cone.

Answer: V = (1/3)πr^2h

Question 2: Calculate the volume of a cone with radius 3 cm and height 9 cm. Use π ≈ 3.14.

Answer: 254.34

Question 3: A cone has a slant height of 13 cm and a radius of 5 cm. Find its vertical height.

Answer: 12

Question 4: Calculate the surface area of a cone with radius 4 cm and height 9 cm. Use π ≈ 3.14.

Answer: 125.44

Question 5: Plot the graph of y=2x for x between -5 and 5 on the grid.

Answer: Students draw on grid

Question 6: Construct a cone with a radius of 2 cm and a height of 6 cm. Show all steps.

Answer: Constructed cone on grid with labeled radius and height

Question 7: A cake is shaped like a cone with radius 10 inches and slant height 15 inches. Find the vertical height of the cake.

Answer: 12 inches

Question 8: Calculate the lateral surface area of a cone with radius 7 cm and height 24 cm. Use π ≈ 3.14.

Answer: 485.44

Question 9: A cone's surface area is 150π cm², and its radius is 5 cm. Find its slant height.

Answer: 15

Question 10: A student incorrectly uses the formula V = πr^2h for the volume of a cone. Explain why this is incorrect and what the correct formula should be.

Answer: Because the volume of a cone is (1/3)πr^2h, not πr^2h.

Question 11: A cone with radius 6 cm has a volume of 288π cm³. Find its height.

Answer: 8

Question 12: Challenge: Derive the formula for the surface area of a cone starting from basic principles.

Answer: Students should explain that Surface Area = πr(l) + πr^2, where l is slant height, with derivation steps.