Question : A solid hemisphere has a radius 21 cm. It is melted to form a cylinder such that the ratio of its curved surface area to total surface area is 2 : 5, What is the radius (in cm) of its base (take $\pi=\frac{22}{7}$ )?

Option 1: 23

Option 2: 21

Option 3: 17

Option 4: 19

Question : If the numerical value of twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume, then what is the numerical value of the radius of the base of the cylinder?

Option 1: 2

Option 2: 3

Option 3: 5

Option 4: 4

Question : The curved surface area of a right circular cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.

Option 1: 8 m

Option 2: 0.04 m

Option 3: 0.08 m

Option 4: 0.008 m

Question : The radius of the base of a solid cone is 9 cm, and its height is 21 cm. It was cut into three parts by two cuts, which were parallel to its base. The cuts are at a height of 7 cm and 14 cm from the base, respectively. What is the ratio of the curved surface area of the top, middle, and bottom parts, respectively?

Option 1: $1 : 4: 8$

Option 2: $1 : 3: 5$

Option 3: $1 : 3: 9$

Option 4: $1: 6: 12$

Question : The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm². If the radius of its base is 7 cm, then what is the volume of this cylinder? (use $\pi=\frac{22}{7}$)

Option 1: 2060 cm³

Option 2: 2480 cm³

Option 3: 3080 cm³

Option 4: 2760 cm³