Question 1: Calculate the volume of a cylinder with a radius of 3 cm and height of 10 cm using π ≈ 3.14.

Answer: 282.6

Question 2: A cylindrical tank has a radius of 4 meters and a height of 6 meters. Calculate its volume, using π ≈ 3.14.

Answer: 301.6

Question 3: A cylinder has a radius of 5 cm and a volume of 392.5 cm³. Find the height of the cylinder, using π ≈ 3.14.

Answer: 5

Question 4: Construct a cylinder on the grid with a radius of 2 units and a height of 6 units. Calculate its volume.

Answer: 50.24

Question 5: Plot the graph of y = 2πr for r from 1 to 5, showing the relationship between radius and the surface area of the base.

Answer: Graph plotted on grid

Question 6: A cylinder has a radius of 3 cm and height of 12 cm. Calculate its volume, using π ≈ 3.14.

Answer: 339.3

Question 7: A cylindrical water tank has a radius of 2.5 meters and a height of 4 meters. Calculate its volume.

Answer: 78.5

Question 8: A student calculates the volume of a cylinder as 150 cm³, given radius 3 cm. Identify and correct any mistake in the calculation.

Answer: Incorrect, because volume = πr²h, so h should be (150)/(π*3²) ≈ 5.3 cm

Question 9: A cylindrical container has a radius of 4 cm and a height of 8 cm. Calculate the volume and then determine how much space is left if it is partially filled to a height of 5 cm.

Answer: Volume full = 402.1 cm³; volume at height 5 = 251.3 cm³

Question 10: Challenge: Derive the formula for the volume of a cylinder starting from the area of the base and integrating over height.

Answer: The volume V = base area × height = πr²h

Question 11: A cylindrical pipe has a radius of 7 cm. Find the height of the pipe if its volume is 1540 cm³, using π ≈ 3.14.

Answer: 10