recallin that, the diameter is twice as long as the radius, namely the radius is half the diameter, so, if the diameter is doubled, the radius is also doubled.
[tex]\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\quad
\begin{cases}
r=radius\\
h=height\\
-----\\
r=\stackrel{doubled}{2r}
\end{cases}\implies V=\pi (2r)^2 h
\\\\\\
V=\pi (2^2r^2)h\implies V=\pi 4r^2 h\implies V=4~(\pi r^2 h)[/tex]
notice, the new volume is 4 times (πr² h), namely 4 times the original.
