Question

The height of a cone is 32cm. a small cone is cut off at the top by a plane parallel to its base. if its volume is 1/64 of the volume of the given cone, at what height above the base is the cone cut?( pi=22/7)

Answer 1

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'

$VO/VO' = OA/OA' =>> 30/h = r/r'$

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