A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. Find the ratio of the volume of the smaller cone to the whole cone.

Let’s draw the figure with the help of the given information,

Let’s suppose the height of the whole cone = h

Radius of the whole cone = R

Given,

The cone is divided into two parts by drawing a plane through the mid-point of cone’s height and parallel to its base.

Since the cone is cut from the middle, here we get;

MR = RP = h/2 cm

Now,

Let’s take the Radius of small cone = r

In ∆MRS and ∆MPQ,

∠MRS = ∠MPQ

∠RMS = ∠PMQ

∴ ∆MRS ∼∆MPQ by AA Similarity Criteria

…….. [Corresponding Sides are proportional]

⇒ R = 2r

Calculate the Volume;

Volume of the smaller cone =

Volume of the whole cone =

Now, Ratio of volumes;

∴

Hence the ration of the smaller cone to the whole cone = 1:8