Question 1: Calculate the volume of a cylinder with radius 5 cm and height 10 cm. Use π ≈ 3.14.

Answer: 785.0

Question 2: Find the surface area of a cylinder with radius 3 meters and height 7 meters. Use π ≈ 3.14.

Answer: 188.52

Question 3: A cylindrical can has a radius of 4 cm and height of 12 cm. How much material is needed to make the can's surface (the total surface area)?

Answer: 226.2

Question 4: A cylindrical tank holds 150 liters of water. If the tank has a radius of 1.5 meters, what is its height? (1 liter = 1 cubic decimeter).

Answer: 20

Question 5: Construct a cylinder with a height of 8 cm and a volume of 1000 cm³. Show your work and label the radius.

Answer: radius = 6.3 cm (approx.)

Question 6: Explain why two cylinders with the same volume can have different surface areas. Provide an example with specific dimensions.

Answer: Different surface areas result from differences in height and radius; larger radius with shorter height can have a smaller surface area than a taller, thinner cylinder with the same volume.

Question 7: A cardboard sheet is used to make a cylindrical container with a diameter of 10 cm and height of 15 cm. Calculate the total amount of cardboard needed.

Answer: 471 cm²

Question 8: A student calculates the volume of a cylinder as 500 cm³ but forgets to square the radius. What common mistake might lead to this incorrect answer?

Answer: Using the formula V = π r h instead of V = π r^2 h, forgetting to square the radius.

Question 9: A cylinder's radius is increased by 50%, and its height remains the same. How does this affect the volume? Provide a ratio.

Answer: Volume increases by 125% (or 1.25 times).

Question 10: Challenge: Derive a formula for the surface area of a cylinder in terms of its volume and radius, assuming height is proportional to radius. State assumptions clearly.

Answer: Assuming height h = k r, then surface area = 2π r^2 + 2π r (k r) = 2π r^2 + 2π k r^2 = 2π r^2 (1 + k).

Question 11: A cylinder with radius 2 m and height 5 m is shown to have a surface area of 88.96 m². Identify and explain a common mistake that could lead to this incorrect value.

Answer: Miscalculating the lateral surface area or using incorrect π value, leading to underestimation.