Solution,

Given,

Diameter of base (d) = 14 cm

∴ Radius of base (r) = 7 cm

Volume of cylinder (v) = 2156 cm^{3}

Now using the formula,

Volume of cylinder (V) = πr^{2}h

Or, 2156 = πr^{2}h

Or, 2156 = π(7)^{2}h

Or, \(2156=\frac{22}77^2h\)

Or, \(2156=22\times7\times h\)

Or, \(h=\frac{2156}{22\times7}\)

Or, h = 14

∴ Height of the cylinder (h) = 14 cm.