Question 1: Calculate the height of a cone with a radius of 3 cm and a slant height of 5 cm.

Answer: 4 cm

Question 2: Find the volume of a cone with radius 4 m and height 9 m. Use π ≈ 3.14.

Answer: 150.8 m^3

Question 3: Construct a cone on the grid with a radius of 2 cm and a height of 6 cm. Show your drawing.

Answer: Student's construction

Question 4: A science experiment involves a cone-shaped funnel with a radius of 5 cm and a height of 12 cm. Calculate its lateral surface area using π ≈ 3.14.

Answer: 392.5 cm^2

Question 5: A cone-shaped container is filled with liquid. If the radius is 3 cm and the volume is 84.78 cm^3, find the height of the liquid level inside.

Answer: 6 cm

Question 6: In a science experiment, a cone is made from paper with a slant height of 7 cm and radius of 4 cm. Calculate the total surface area of the cone.

Answer: 113.04 cm^2

Question 7: A student constructs a cone with a radius of 3 cm and a height of 9 cm. If they mistakenly use a slant height of 10 cm, identify and explain the mistake in their calculation of the lateral surface area.

Answer: They used the wrong slant height, leading to an incorrect lateral surface area. Correct slant height should be 9.5 cm based on Pythagoras.

Question 8: A science experiment involves a cone with radius 2.5 cm and height 8 cm. Calculate the total surface area, including the base.

Answer: 61.41 cm^2

Question 9: A cone-shaped sculpture has a radius of 6 inches and a slant height of 10 inches. Determine the volume of the sculpture in cubic inches, using π ≈ 3.14.

Answer: 226.08 in^3

Question 10: Challenge: A conical glass has a radius of 4 cm and slant height of 10 cm. If the height is doubled, how does this affect the volume? Explain your reasoning.

Answer: Doubling the height quadruples the volume because volume is proportional to height, so volume increases by a factor of 2^3 = 8.