Let VAB be a cone of height 32cm and base r cm . Suppose it is cut off by a plane parallel to the base at a height H from the base of the cone.
ΔVOA ≈ Δ VO'A'
[tex]VO/VO' = OA/OA' =>> 30/h = r/r'[/tex]
It is given that
Volume of cone VA'B' = 1/64 Volume of cone VAB
1/3 π r₁²h₁ = 1/64 × 1/3 π r² × 32
r₁² h₁ = 1
r² 2
( r¹ )² × h = 1
( r ) 2
h₁³ = 1
1024 2 ( r = 32 , r² = 32² = 1024)
h₁³ = 512
h₁ = 8 cm
H = 32 - h₁
H = 32 - 8 = 24cm
