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Question

The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to the base. If the volume of the small cone be 164 of the volume of the given cone, at what height ( in cm) above the base is the section made ?


A

20

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B

30

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C

40

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D

50

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Solution

The correct option is B

30



Let R be the radius of the given cone, r the radius of the small cone, h be the height of the frustum and h1 be the height of the small cone.

In the figure,ONCOMA

ONOM=NCMA [Sides of similar triangles are proportional]

h140=rR

h1=(rR)×40 .......(i)

We are given that Volume of small conevolume of given cone=164

13πr2×h113πR2×40=164

r2R2×140×[(rR)40]=164 [ By (i) ]

(rR)3=164=(14)3

rR=14 ...... (ii)

From (i) and (ii) h1=14×40=10 cm

,h=40h1=(4010) cm

h=30 cm

Hence, the section is made at a height of 30 cm above the base of the cone .


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