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# The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

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Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.3 mensuration.

we have to find the The height of a cone is 20 cm.
A small cone is cut off from the top by a plane
parallel to the base. If its volume be 1/125 of the
volume of the original cone.

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### 1 Answer

1. Let the radius of the small cone be r cm

Radius if the big cone = R cm

Given, height of the big cone = 20 cm

Let the height of section made = h cm

Then, the height of small cone will be = (20 â€“ h) cm

Now,

In â–³OAB and â–³OCD

âˆ AOB = âˆ COD [common]

âˆ OAB = âˆ OCD [each 90o]

Then, OAB ~ â–³OCD [by AA similarity]

So, by C.P.S.T we have

OA/ OC = AB/ CD

(20 â€“ h)/ 20 = r/ R â€¦â€¦ (i)

Also given,

Volume of small cone = 1/125 x volume of big cone

1/3 Ï€ r2(20 â€“ h) = 1/125 x 1/3 Ï€R2 x 20

r2/ R2 = 1/125 x 20/ (20 â€“ h) [From (i)]

(20 â€“ h)2/ 202 = 1/125 x 20/20 â€“ h

(20 â€“ h)3 = 203/ 125

20 â€“ h = 20/5

20 â€“ h = 4

h = 20 â€“ 4 = 16 cm

Therefore, itâ€™s found that the section was made at a height of 16 cm above the base.

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