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The height of a cone is …

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The height of a cone is 24 cm.A small cone is cut off at the top by a plane parallel to the base.If the volume of the remaining part be 7/8of the given cone, at what height above the base is the section made?

  • 1 answers

Naveen Sharma 7 years, 2 months ago

Ans.

So h/24 = r/R

h = 24r/R ..... (1)

Volume of Cone ABC =  24πR2/3  = 8πR2      ----- (2)

Remaining Portion is Know as Frustum as its volume is 7/8 of Cone ABC. 

So Volume of Smaller Cone A`B`C` = 1/8 of Cone ABC

Volume of Cone A`B`C`  =  π r2h / 3 

from (1),   

π r224r/3R  =  8π r3/R ------ (3)

Accroding to questions

8π r3/R  = 8πR2/8

8π r3/R = πR2

r3/R3 = 1/8

r/R = 1/2

put this value in (1)

We get h = 24*1/2 = 12cm

So cone is cut from the height 24-12 = 12 cm

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