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प्रश्न
A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is
विकल्प
A. 1 : 2
B. 1 : 4
C. 1 : 6
D. 1 : 8
उत्तर
Let the height and the radius of whole cone be H and R respectively.
The cone is divided into two parts by drawing a plane through the mid point of its height and parallel to the base.
Let the radius of the smaller cone be r cm.
In ∆OCD and ∆OAB,
∠OCD = ∠OAB (90°)
∠COD = ∠AOB (Common)
∴∆OCD ∼ ∆OAB (AA Similarity criterion)
⇒ R = 2r
Thus, the ratio of smaller cone to whole cone is 1 : 8.
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