Ramdom
Geometry
Level
3
A cone is divided into two parts by drawing a plane through the mid-point of its axis parallel to its base.Then the ratio of volumes of the two parts is :
2 : 7
3 : 2
1 : 7
7 : 2
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1 solution
Let the
height of the larger cone = 2x
Radius of the larger cone = 2y
Vol of the larger cone, v1 = 1/3.π .(2y)^2.2x = 1/3.π .8(x^2)y
height of the smaller cone = x
radius of the smaller cone = y
vol of the smaller cone = 1/3.π /x^2.y
Vol of the 2nd part of the cone = 1/3.π .x^2.y(8-1) = 1/3.π .7.x^2.y
∴ Ratio = (1/3. π .x^2.y)/(1/3. π.7.x^2.y)= 1:7