For a right circular cone, the ratio of the slant height to the length of the radius is 5 : 3.

Question

For a right circular cone, the ratio of the slant height to the length of the radius is 5 : 3. If the volume of the cone is 768𝜋 in³, find the lateral area (in square inches) of the cone.

Answer 1

V = 1/3πr²l, l/r = 5/3, l= 5r/3; V = 1/3πr²·5r/3 = 5πr³/9 = 768π; r = (768·9/5)^1/3 = 11.14 in;

l5·11.14/3 = 18.57 in

So, lateral surface S = πrl = π·11.14in·18.57in = 649.9 in².