Base area of the cone, πr2 = 38.5 cm2
Volume of the cone, V = 1/3 πr2h = 77
πr2 = 38.5
22/7 r2= 38.5
r2 = 38.5 x 7/22
r2 = 12.25
r =√12.25 = 3.5
V= 1/22 x 22/7 x 3.5 x 3.5 x h = 77
∴ h = \(\frac {77\times3\times7}{22\times12.25}\) = 6
∴ Height of the cone = 6 cm