Question : A sphere and another solid hemisphere have the same surface area. The ratio of their volumes is:

Option 1: $2 \sqrt{3}: 8$

Option 2: $3 \sqrt{3}: 8$

Option 3: $3 \sqrt{3}: 4$

Option 4: $\sqrt{3}: 4$

Question : The radius of the ends of a frustum of a solid right-circular cone 45 cm high is 28 cm and 7 cm. If this frustum is melted and reconstructed into a solid right circular cylinder whose radius of base and height are in the ratio 3: 5, find the curved surface area (in ${cm}^2$ ) of this cylinder. [Use $\pi=\frac{22}{7}$.]

Option 1: 4580

Option 2: 4610

Option 3: 4640

Option 4: 4620

Question : The curved surface area and circumference at the base of a solid right circular cylinder are 2200 cm² and 110 cm, respectively. Find the height of the cylinder.

Option 1: 24 cm

Option 2: 22 cm

Option 3: 20 cm

Option 4: 18 cm

Question : The total surface area of a right circular cylinder is 1848 cm². The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)

Option 1: 4312 cm³ 

Option 2: 3696 cm³ 

Option 3: 4002 cm³ 

Option 4: 4851 cm³ 

Question : The height and curved surface area of a right circular cylinder are $7~\text{cm}$ and $70\pi~\text{cm}^2$. Its total surface area is:

Option 1: $140 \pi~\text{cm}^2$

Option 2: $150 \pi~\text{cm}^2$

Option 3: $180 \pi~\text{cm}^2$

Option 4: $120 \pi~\text{cm}^2$