Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

The height of a cone is $30 cm$ . A small cone is cut off at the top by a plane parallel to the base. If its volume be $1 / 27$ of the volume of the given cone at what height above the base is the section made?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

18 cm

15 cm

11 cm

10 cm

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that height of the cone is H=30cm.
Let the radius of the big and small cone be

R

and r .
It is also given that the volume of smaller cone is

127

of the given cone.
The volume of a cone is expressed as,

V = 13 π r 2 h

, where

r

and h be the radius and height of a cylinder.
The required figure is shown below,
Question Image

So,

V 2 V 1 = 127 ⇒ 13 π r 2 h 13 π R 2 H = 127 ⇒ 13 π r 2 h 13 π R 2 30 = 127 ⇒ r 2 h 30 R 2 = 127 ..... 1

From the figure,

⇒ r R = h 30

So, from the equation (1),
Question Image

Thus, the height is 10cm.
Therefore, option (4) is correct.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE