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A cone of radius 8 cm and height 12 cm ...

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane thrpugh the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

Text Solution

Verified by Experts

We can solve this using similarity
Let r and h be the radius and height of a cone OAB
Let `OE=(h)/(2)`
As OED and OFB are similar
there `(OE)/(OF)=(ED)/(FB) (h//2)/(h)=(ED)/(r )`
`ED=(r )/(32)`
Now volume of cone IOCD `=(1)/(3)pir^(2)h=(1)/(3)xxpixx((r)/(2))^(2)xx(h)/(2)=(pir^(2)h)/(24)`
and volume of cone OAB=`(1)/(3)xxpixxr^(2)xxh=(pir^(2)h)/(3)`
`therefore ("volume of part OCB")/("volume of part CDAB")= (pir^(2)h)/((pir^(2)h)/(3))-(pir^(2)h)/(24)=((1)/(24))/((1)/(3))-(1)/(24)=(1)/((24)/((8-21)/(24)))=(1)/(7)`
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