Question : The volume of a solid right circular cone is $600 \pi \;\text{cm}^3$ and the diameter of its base is 30 cm. The total surface area (in cm²) of the cone is:

Option 1: $480 \pi$

Option 2: $255 \pi$

Option 3: $472 \pi$

Option 4: $496 \pi$

Question : The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm³?

Option 1: $192 \pi$

Option 2: $210 \pi$

Option 3: $240 \pi$

Option 4: $180\pi$

Question : The total surface area of a solid metallic hemisphere is 462 cm². This is melted and moulded into a right circular cone. If the radius of the base of the cone is the same as that of the hemisphere, then its height is: (use $\pi=\frac{22}{7}$)

Option 1: 14 cm

Option 2: 7 cm

Option 3: 21 cm

Option 4: 28 cm

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

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