19
Question
If the right circular cone is cut into three solids of volumes V1,V2 and V3 by two cuts which are parallel to the base and trisects the altitude, then V1:V2:V3 is:
If the right circular cone is cut into three solids of volumes V1,V2 and V3 by two cuts which are parallel to the base and trisects the altitude, then V1:V2:V3 is:
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Solution
The correct option is D None of these
Solution: -
The resultant figure is made of three similar triangles. The height and radius will be in ratio 1/3:2/3:1 = 1:2:3.
r1 = 1, h1 = 1
r2 = 2, h2 = 2
r3 = 3, h3 = 3
Volume will be in the ratio of r2h for the three circular cones.
Required Volumes are
V1 = r12 x h1 = 1
V2 = r22 x h2 - V1 = 8 - 1 = 7
V3 = r32 x h3 - (V1 + V2) = 27 - (7 + 1) = 19
Volumes will be in given ratio = 1:7:19. Option (d).
Solution: -
The resultant figure is made of three similar triangles. The height and radius will be in ratio 1/3:2/3:1 = 1:2:3.
r1 = 1, h1 = 1
r2 = 2, h2 = 2
r3 = 3, h3 = 3
Volume will be in the ratio of r2h for the three circular cones.
Required Volumes are
V1 = r12 x h1 = 1
V2 = r22 x h2 - V1 = 8 - 1 = 7
V3 = r32 x h3 - (V1 + V2) = 27 - (7 + 1) = 19
Volumes will be in given ratio = 1:7:19. Option (d).
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