Question

a solid right cylinder 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 _____​

Answer 1

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a solid right cylinder 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 _____

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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.

$\bold{In \: ∆OCD \: and \: ∆OAB,}$

$\bold{∠OCD = ∠OAB  (90°)}$

$\bold{∠COD = ∠AOB  (Common)}$

$\bold{∴∆OCD ∼ ∆OAB  (AA \: Similarity \: criterion)}</p><p>$

$\bold{⇒ R = 2r} \\ </p><p>$

Thus, the ratio of smaller cone to whole cone is 1 : 8.