The radius and height of a right circular cone are in ratio 5:12. If its volume is 314cm³ ,find slant height and curved surface area .(take as 3.14).

Ratio of radius and height = 5:12

Let the radius and height be 5x and 12x respectively

Volume of cone= 314 cm³

1/3r²h= 314

1/3 x 3.14 x (5x)² x 12x= 314

(25x²)(4x) =314/3.14

100x³ = 100

x³=1

x= ³√1

x= 1

Radius = 5x = 5 cm

Height = 12x = 12 cm

l² = h² + r²

l = √{(12)² + (5)²}

l=√(144+25)

l=√169

l= 13 cm

C.S.A of cone = rl

=3.14 x 5 x 13

=204.10 cm²