The curved surface area of a right circular cone is 2310 cm² and its radius is 21 cm. If its radius is increased by 100% and height is reduced by 50%, then its capacity (in litres) will be (correct to one decimal place): $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{Curved surface area of cone}} = \pi rl \cr & \frac{{22}}{7} \times 21 \times l = 2310 \cr & 66l = 2310 \cr & l = 35 \cr & {\text{Height}} = \sqrt {{{35}^2} - {{21}^2}} \cr & = \sqrt {1225 - 441} \cr & = \sqrt {784} \cr & = 28{\text{ cm}} \cr & {\text{New radius}} = 21 + 21 = 42{\text{ cm}} \cr & {\text{New height}} = 28 - 14 = 14{\text{ cm}} \cr & {\text{New volume}} = \frac{1}{3}\pi {r^2}h \cr & = \frac{1}{3} \times \frac{{22}}{7} \times 42 \times 42 \times 14 \cr & = 22 \times 42 \times 28 \cr & = 25872{\text{ c}}{{\text{m}}^3} \cr & {\text{Capacity}} = \frac{{25872}}{{1000}} = 25.9{\text{ litres}} \cr} $$