A cylinder's height is 8 cm and its volume is \(128πcm^3\). If its radius is doubled and its height is cut in half, the volume of the resulting cylinder is _________.

The volume of a cylinder is \(πr^2h\).
In the original cylinder, \(πr^2h = 128π\) so \(r^2(128π/8π) = 16\)
And the radius, r, equals √16 = 4. In the new cylinder, the radius is doubled to 8 and the height is cut in half to 4.
The resulting volume is \(π × 8^2 × 4 = 256πcm^3\).