Question 1: Calculate the surface area of a cylinder with radius 5 cm and height 10 cm using the formula 2πr² + 2πrh.

Answer: Approximate value

Question 2: A cylindrical can has radius 3 inches and height 8 inches. Find its surface area.

Answer: Approximate value

Question 3: Explain why the term 2πr² appears in the surface area formula for cylinders.

Answer: It accounts for the areas of both circular ends of the cylinder.

Question 4: A storage tank is in the shape of a cylinder with radius 4 m and height 12 m. Calculate its surface area.

Answer: Approximate value

Question 5: If a cylinder's radius is doubled while its height remains the same, how does the surface area change? Show your reasoning.

Answer: Surface area increases by a factor of 4.

Question 6: A cylinder has a surface area of 628.32 cm². If the radius is 4 cm, find its height.

Answer: Approximate value

Question 7: Construct a diagram of a cylinder on the grid paper, then shade the areas representing the top and side surfaces.

Answer: Diagram with shaded top circle and rectangular side

Question 8: Calculate the surface area of a cylinder with radius 7 meters and height 3 meters.

Answer: Approximate value

Question 9: A water tank is a cylinder with radius 2.5 meters and height 10 meters. Due to a redesign, the radius is increased to 3 meters. Find the new surface area and explain the change.

Answer: Approximate value; surface area increases due to larger radius.

Question 10: Identify and correct the mistake in this calculation: Surface area = 2π(4)² + 2π(4)(10) = 2×3.14×16 + 2×3.14×4×10 = 100.48 + 251.2 = 351.68 cm².

Answer: Incorrect addition; should be 2πr² + 2πrh, not adding the terms directly.

Question 11: Challenge: Derive the formula for the surface area of a cylinder starting from the area of its components.

Answer: Sum of areas: 2πr² for two circles + 2πrh for the side.