A solid metallic right circular cylinder of base diameter 16 m and height 2 cm is melted and recast into a right circular cone of height three times that of the cylinder. Find the curved surface area of the cone. [Use $$\pi $$ = 3.14]
a) 196.8 cm²
b) 228.4 cm²
c) 251.2 cm²
d) None of these

Answer: c
Explanation: Let the radius of the cone be r cm
$$\eqalign{ & \pi \times {\left( 8 \right)^2} \times 2 = \frac{1}{3} \times \pi \times {r^2} \times 6 \cr & \Rightarrow r = 8 \cr} $$
Slant height,
$$\eqalign{ & l = \sqrt {{r^2} + {h^2}} \cr & \,\,\, = \sqrt {{8^2} + {6^2}} \cr & \,\,\, = \sqrt {100} \cr & \,\,\, = 10\,cm \cr} $$
Curved surface area of cone :
$$\eqalign{ & = \pi rl \cr & = \left( {3.14 \times 8 \times 10} \right){\text{ c}}{{\text{m}}^2} \cr & = 251.2{\text{ c}}{{\text{m}}^2} \cr} $$