Let us assume the height and radius of the original cylinder is l and r respectively.

Let V₁ be the original volume and V₂ be the volume after the change in height and radius.

Therefore volume of the original cylinder is given by: $V=\pi r^{2}l$

After, height of a cylinder becomes $\frac{1}{8}$of the original height and the radius is doubled

We have, $r_2=2rand{l}_2=\frac{l}{8}$

So the new volume is given by:

$V_2=\pi r_2^2{l}_2=\pi \left(2r{)}^2\right(\frac{l}{8})$

$\Rightarrow V_2=\frac{4\pi r^{2}l}{8}$

$\Rightarrow V_2=\frac{\pi r^{2}l}{2}=\frac{V_1}{2}$

$\Rightarrow V_2=\frac{V_1}{2}$
Hence the volume of the cylinder will be halved.