Question 1: Calculate the surface area of a cylinder with a radius of 5 cm and a height of 12 cm. Use π ≈ 3.14.

Answer: The surface area is approximately 471.2 cm².

Question 2: A cylindrical can has a radius of 3 cm and a height of 10 cm. Calculate its volume. (Use π ≈ 3.14)

Answer: The volume is approximately 282.6 cm³.

Question 3: Construct a cylinder on the grid with a radius of 4 cm and a height of 9 cm. Label the dimensions clearly.

Answer: Constructed with radius 4 cm and height 9 cm.

Question 4: A cylindrical water tank has a volume of 1500 cm³ and a height of 15 cm. Find its radius. (Use π ≈ 3.14)

Answer: Radius is approximately 6.19 cm.

Question 5: If the radius of a cylinder is doubled while keeping the height the same, by what factor does the surface area increase?

Answer: Surface area increases by a factor of 4.

Question 6: A cylindrical pipe has a diameter of 8 cm and a length of 50 cm. Calculate the total surface area including the ends. Use π ≈ 3.14.

Answer: Surface area is approximately 502.4 cm².

Question 7: A factory produces cylindrical rods with a radius of 2.5 cm and a length of 30 cm. How many such rods can be made from a bulk material of 6000 cm³? (Ignore waste and overlaps)

Answer: Number of rods is 8.

Question 8: Identify and correct the mistake in the following statement: "The surface area of a cylinder is found by adding twice the area of the base and the lateral surface area."

Answer: Correct statement; no mistake.

Question 9: A cylindrical storage tank has a diameter of 14 m and a height of 10 m. Calculate the volume of the tank in cubic meters.

Answer: Volume is approximately 1540 m³.

Question 10: Explain how changing the radius of a cylinder affects its surface area and volume, assuming the height remains constant.

Answer: Increasing radius increases both surface area and volume; volume increases proportionally to the square of the radius, surface area increases proportionally to the radius.

Question 11: A cylindrical drum has a radius of 1.2 m and a height of 2.5 m. Calculate its surface area, including the top and bottom.

Answer: Surface area is approximately 21.24 m².

Question 12: A student claims that the volume of a cylinder is always greater than its surface area. Is this true? Explain your reasoning.

Answer: No, the volume and surface area depend on dimensions; for small cylinders, surface area can be larger than volume.