Question : The radius of the base of a cylindrical tank is 4 m. If three times the sum of the areas of its two circular faces is twice the area of its curved surface, then the capacity (in kilolitres) of the tank is:

Option 1: $54 \pi$

Option 2: $144 \pi$

Option 3: $96 \pi$

Option 4: $108 \pi$

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 cone is 2310 cm$^2$ and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be (correct to one decimal place): (Take $\pi=\frac{22}{7}$)

Option 1: 27.8

Option 2: 28.2

Option 3: 26.7

Option 4: 25.9

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 : The volume of a solid right circular cylinder of height 8 cm is $392 \pi$ cm³. Its curved surface area (in cm²) is:

Option 1: $161 \pi$

Option 2: $96 \pi$

Option 3: $210 \pi$

Option 4: $112 \pi$

Question : The radius of a solid right circular cone is 36 cm and its height is 105 cm. The total surface area (in cm²) of the cone is:

Option 1: $4296 \pi$

Option 2: $3996 \pi$

Option 3: $5292 \pi$

Option 4: $3969 \pi$