Question

A composite figure is formed from a cone and a cylinder with the same base radius, and its volume can be calculated by multiplying the volume of the cylinder by a rational number, a/b. What arrangements of the cylinder and cone could explain this?

Answer 1

The composite figure comprises of a cone balanced on top of  cylinder

Step-by-step explanation:

The composite figure is formed from a cone and a cylinder with the same base radius, Let the base radius be r

Then the volume of the cone will be $V_{cone}$

Then the volume of the cylinder will be $V_{cylinder}$

$V_{cylinder} = \pi r^{2} h_{cylinder}$

The total volume of the composite figure will be V, where

$V= V_{cone} + V_{cylinder}$

$V = \frac{1}{3} \pi r^{2} h_{cone} +\pi r^{2} h_{cylinder}$

let the height of cone and cylinder be same

The volume of the composite figure will be $\frac{4}{3} \pi r$$r^{2} h$

Hence $\frac{4}{3} = \frac{a}{b}$

Thecomposite figure comprises of a cone balanced on top of  cylinder