Question : From a solid cylindrical wooden block of height 18 cm and radius 7.5 cm, a conical cavity of the same height and radius is taken out. What is the total surface area (in cm²) of the remaining solid?

Option 1: $270 \pi$

Option 2: $416.25 \pi$

Option 3: $326.25 \pi$

Option 4: $472.5 \pi$

Question : A conical vessel (solid) is made of iron. Its base radius is 7 cm and its height is 15 cm. If the weight of the iron per cubic centimetre is 15 g, what is the weight of the vessel?

Option 1: 13.55 kg

Option 2: 12.55 kg

Option 3: 14.55 kg

Option 4: 11.55 kg

Question : A hollow sphere has an outer radius of 6 cm and inner radius of 3 cm. What is the volume of this hollow sphere?

Option 1: 252$\pi$ cm³

Option 2: 356$\pi$ cm³

Option 3: 144$\pi$ cm³

Option 4: 175$\pi$ cm³

Question : A cylindrical tube, open at both ends, is made of a metal sheet which is 0.5 cm thick. Its outer radius is 4 cm and its length is 2 m. How much metal (in cm$^3$) has been used in making the tube?

Option 1: $800 \pi$

Option 2: $450 \pi$

Option 3: $750 \pi$

Option 4: $550 \pi$

Question : The area of the sector of a circle of radius 12 cm is $32 \pi \;\mathrm{cm}^2$. Find the length of the corresponding arc of the sector.

Option 1: $\frac{16}{3} \pi$ cm

Option 2: $\frac{13}{3} \pi$ cm

Option 3: $\frac{10}{3} \pi$ cm

Option 4: $\frac{8}{3} \pi$ cm