Question

A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by a plane parallel to its base. Find the ratio on the volumes of two parts of the cone.

Answer 1

Given: 

let the height of the cone be H and its base radius be R 

This cone is divided into two parts through the mid-point of the height of the cone such that 

ED||BC

Therefore 

triangle AED is similar to triangle ABC 

By the condition of similarity, 

\(\frac{OE}{PC}\) = \(\frac{AO}{AP}\) = \(\frac{AO}{2AO}\)

⇒ \(\frac{OE}{R}\) = \(\frac{1}{2}\) ⇒ OE = \(\frac{R}{2}\)

Volume of a cone = \(\frac{1}{3}\) πr²h 

Volume of the frustum = Volume of the cone ABC – Volume of the cone AED