If the area of the base of a right circular cone is 3850 cm² and its height is 84 cm, then the curved surface area of the cone is :
a) 10001 cm²
b) 10010 cm²
c) 10100 cm²
d) 11000 cm²

Answer: b
Explanation:
$$\eqalign{ & \pi {r^2} = 3850 \cr & \Rightarrow {r^2} = \left( {\frac{{3850 \times 7}}{{22}}} \right) = 1225 \cr & \Rightarrow r = 35 \cr & {\text{Now, }}r = 35{\text{ cm, }}h = 84{\text{ cm}} \cr & {\text{So,}} \cr & l = \sqrt {{{\left( {35} \right)}^2} + {{\left( {84} \right)}^2}} \cr & l = \sqrt {1225 + 7056} \cr & l = \sqrt {8281} \cr & l = 91{\text{ cm}} \cr} $$
Curved surface area :
$$\eqalign{ & = \left( {\frac{{22}}{7} \times 35 \times 91} \right){\text{ c}}{{\text{m}}^2} \cr & = 10010{\text{ c}}{{\text{m}}^2} \cr} $$