Let the radius of thesmall cone be r cm
Radius if the big cone= R cm
Given, height of thebig cone = 20 cm
Let the height ofsection made = h cm
Then, the height ofsmall cone will be = (20 тАУ h) cm
Now,
In тЦ│OAB and тЦ│OCD
тИаAOB = тИаCOD [common]
тИаOAB = тИаOCD [each 90o]
Then, OAB ~ тЦ│OCD [by AA similarity]
So, by C.P.S.T we have
OA/ OC = AB/ CD
(20 тАУ h)/ 20 = r/ R тАжтАж(i)
Also given,
Volume of small cone =1/125 x volume of big cone
1/3 ╧А r2(20тАУ h) = 1/125 x 1/3 ╧АR2┬аx 20
r2/ R2┬а=1/125 x 20/ (20 тАУ h) [From (i)]┬а
(20 тАУ h)2/202┬а= 1/125 x 20/20 тАУ h
(20 тАУ h)3┬а=203/ 125
20 тАУ h = 20/5
20 тАУ h = 4
h = 20 тАУ 4 = 16 cm
Therefore, itтАЩs foundthat the section was made at a height of 16 cm above the base.