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If a cone is cut into two parts by a horizontal plane passing through the mid points of its axis,then what is the ratio of the volumes of upper and lower part?

If a cone is cut into two parts by a horizontal plane passing through the mid points of its axis,then what is the ratio of the volumes of upper and lower part?

Grade:10

1 Answers

Arun
25763 Points
3 years ago
If we cut cone from midpoint then
use similarly concept.
let r is radius of above part and R is the radius of base of cone.
R/r=h/(h/2)=2/1
R=2r
now 
volume of cone =πR2h
=π(2r)2h=4πr2h volume of small cone =πr2h/2
now,
volume of below part =4πr2h-πr2h/2
=7/2 πr2
now ratio = volume of above part/volume of below part
=(πr2h/2)/(7/2πr2h)=1/7
hence ratio =1:7

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