Question

The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is $\frac{1}{64}th$ the volume of original cone. The height from the base at which the section is made is:

Answer 1

It is given that the height of a cone = 60 cm

The volume of a small cone cut on the top by plane parallel to base of given cone
= volume of given cone

We have to find the height from the base at which section is made.

Let R be the radius of base of given cone

Let H be the height of given cone

H = 60 cm

Let r be the radius of base of small cone

Let h be the height of small cone

In ΔAPC and ΔAQE

PC || QE

Therefore

Hence ΔAPC ~ ΔAQE

…… (1)

[From (1)]

Hence Option (c) is correct.