# Why is the extension of a uniformly tapered round bar greater than that of a uniform cylindrical bar?

A round bar, of Length $$L$$ and young's modulus $$E$$, tapers uniformly from radius $$r_1$$ to radius $$r_2=2r_1$$. The extension produced by a tensile axial load $$P$$ is equal to $$\frac{PL}{2\pi E r_1^2}$$.

Comparing its extension to that of a uniform cylindrical bar having a radius equal to the mean radius of the tapered bar ($$\frac{3}{2}r_1$$), the extension of the cylindrical bar is equal to $$\frac{8}{9}$$ times extension of tapered bar.

I understand the calculations and the derivation of the above results, but I would like to know the reason of why do tapered objects deform more than untapered objects.