Question

an hollow cone is cut by a plane paralel to the base and the upper portion is removed. curved surface area of the remainder is 8/9 of the curved surface of the whole cone.find the ratio of the line segment into which the cones altitude is divided by the plane?

Answer 1

Csa of frustum=8/9 Csa of cone
(R-r) (L-l) =8/9πRL
(R-r/R)(L-l/L)=8/9
(1+h/H)(1-h/H)=8/9
1-h square/H square = 8/9[sorry not able to write square properly ]
h square/Hsquare=8/9
h/H=1/3
H=3
Ratio=h/H-h=h/3h-h=1/2