Question

The radius and the height of a right circular cone are in the ratio pf 5:12 and its volume is 2512cu cm . find the curved surface area and the total surface area of the cone (Π= 3•14)

Answer 1

let r is the radius and h is the height of cone ,
a/c to question ,
r/ h = 5/12
r =5h/12
now,
volume of cone = πr^2h/3
2512 cm^3 = π(5h/12)^2h/3
=> 2512 =3.14 x 25/144 x 1/3 x h^3
=> 314 x 8 = 3.14 x (25/3 x 144) h^3
=> 4 x 8 x 144 x 3 = h^3
=> h^3 = 4 x 4 x 4 x 4 x 2 x 3 x 3 x 3
=> h = 4 x 2 x 3 = 24 cm

so, r = 5/12 x 24 = 10 cm

now,
l =√(h^2 + r ^2) = 26 cm

now ,
surface area of cone =π r l
=3.14 x 10 x 26
=816.4 cm^2