Q. 314.8( 6 Votes )

# <span lang="EN-US

Answer :

Given height of cone, H= 30 cm

Let radius of the cone be R. Let cone of height h be cut off from the top of the given cone and radius be r.

Consider ΔAPC and ΔAQE,

PC || QE

ΔAPC ~ ΔAQE

AP/PQ = PC/QE

h/H = r/R … (1)

Given, Volume of smaller cone = 1/27 (Volume of given cone)

So, Volume of cone ABC = 1/27 (Volume of cone ADE)

Volume of cone ABC / Volume of cone ADE = 1/27

We know that volume of cone = πr2h/3

So,

(πr2h/3) / (πR2H/3) = 1/27

(r/R)2(h/H) = 1/27

From (1),

(h/H)2(h/H) = 1/27

(h/H)3 = 1/27

h/H = 1/3

h = (1/3) H

h = (1/3) (30)

h = 10 cm

Now, PQ = H – h = 30 – 10

PQ = 20 cm

Ans. The height at which the cone is cut from its base is 20 cm.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 