Question

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

Answer 1

let r be radius l be slant height,h be height of cone.
\[volume V=\frac{ 1 }{ 3 }\pi r^2 h\]
\[lateral ~ area~A=\pi rl\]
h=9
\[V=\frac{ 1 }{ 3 }\pi r^2*9=3\pi r^2\]
\[\pi r l=3 \pi r^2\]
\[\frac{ \pi r l }{ \pi r^2 }=3,\frac{ l }{ r }=3\]

Answer 2

now find the ration of l and r