Question

16) The height of cone. is loum. The cone is
divided into two parts using a plane parallel
to its base at the middle of its height
Find the ratio of the volumes of the two
parts .
5cm
foam ty
5 cm.​

Answer 1

Answer:

Step-bLet the height and radius of the given cone be H and R respectively.

Upper part is a smaller cone and the bottom part is the frustum of the cone.

⇒ OC = CA = h/2

Let the radius of smaller cone be r cm.

In ΔOCD and ΔOAB,

∠OCD = ∠OAB = 90°

∠COD = ∠AOB (common)

∴ ΔOCD ∼ ΔOAB (AA similarity)

⇒ OA/OC = AB/CD = OB/OD

⇒ h / h/2 = R/r

⇒ R = 2r

the radius and height of the cone OCD are r cm and h/2 cm

therefore the volume of the cone OCD = 1/3 x π x r x h/2 = 1/6 πr h

Volume of the cone OAD = 1/3 x π x R x h = 1/3 x π x 4r x h

The volume of the frustum = Volume of the cone OAD - Volume of the cone OCD

= (1/3 x π x 4r x h) – (1/3 x π x r x h/2)

= 7/6 πr h

Ratio of the volume of the two parts = Volume of the cone OCD : volume of the frustum

= 1/6 πr h : 7/6 πr h

= 1 : 7