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Question
If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the ratio of the volumes of the upper part and the cone is
Options
1 : 2
1: 4
1 : 6
1 : 8
Solution
Since,
`Delta VOA ∼ Delta VO'C`
Therefore,
In `Delta VOA ` and `Delta VO'C`
`(h/2)/h = (O'C)/(OA)`
`1/2 =(O'C)/(OA)`
`(O'C)/(OA) = 1/2`
The ratio of the volume of upper part and the cone,
`V_1/V_2 = (1/3pi(O'C) xx h/2)/ (1/3pi(OA)^2 xx h)`
`V_1/V_2 = ((O'C)/(OA))^2 xx 1/2 ........... (2)`
From eq. (1) and (2),
We get,
`V_1/V_2 = (1/2)^2 xx 1/2`
`V_1/V_2 = 1/4 xx 1/2`
`V_1 : V_2 = 1 : 8`
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