Question

The height of a cone is $40cm$ A Small cone is cut off at the top by a plane parallel to its base. If its volume be $\frac{1}{64}$ of the volume of the given cone at what height above the base is the section cut?

Answer 1

we have been given the volume scale factor which is 1/64.

According to this ratio, the formula for volume scale factor will be:

Volume of the smaller cone divide by volume of larger cone.

V. S. F=1/64

We get the linear scale factor:

(l.s.f)^3=V.S.F

L.S.F=1/4

L.s.f=height of small cone/height of large cone.

1/4=x/64

64=4x

X=16cm

Height above base where section was made:

40-16=24cm