A cylinder whose height is 8 cm has a volume of \(128πcm^3\). 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 \(π × 8^2 × 4 = 256πcm^3\).