Question : A right circular cylindrical tunnel of diameter 5 cm and length 10 cm is to be constructed from a sheet of iron. The area of the iron sheet required will be:

Option 1: $52\pi \ \text{cm}^2$

Option 2: $50\pi \ \text{cm}^2$

Option 3: $51\pi \ \text{cm}^2$

Option 4: $49\pi \ \text{cm}^2$

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 : Find the total surface area of a sphere whose volume is $\frac{256}{3} \pi \;\text{cm}^3$.

Option 1: $48 \pi \;\text{cm}^2$

Option 2: $64 \pi \;\text{cm}^2$

Option 3: $38 \pi \;\text{cm}^2$

Option 4: $56 \pi \;\text{cm}^2$

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 diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in cm²) of the hemisphere.

Option 1: $25 \pi$

Option 2: $\frac{75 \pi}{4}$

Option 3: $\frac{50 \pi}{4}$

Option 4: $\frac{25 \pi}{4}$

Question : Three metallic spheres of radii 10 cm, 8 cm, and 6 cm, respectively are melted to form a single solid cone of radius 12 cm. Find the curved surface area of the cone, correct to two places of decimal. (Take $\pi=3.14$)

Option 1: $1664.50 \text{ cm}^2$

Option 2: $1669.86 \text{ cm}^2$

Option 3: $1876.79 \text{ cm}^2$

Option 4: $1864.41 \text{ cm}^2$