Question

Find the ratio of the slant height to the radius of a right cicular cone in which the volume and lateral area are numerically equal. Assume the altitude of the cone to be 9 units.

Answer 1

ii) Its lateral surface area = πrl sq. units
Its volume = (1/3)*πr²h = 3πr² cu. units [Since given h = 9 units]

iii) As both the above are numerically equal, πrl = 3πr²
Simplifying, l = 3r

Answer 2

*whispers* The radius is 3:1