The value of k obtained by summing the volumes of the cone and the hemisphere is k = 1296
The steps used to find the value of k are as follows;
The radius of the cone, r = 18 cm/2
r = 9 cm
Volume of the cone, V = (1/3) × π × r² × h
h = 30 cm
Therefore; V = (1/3) × π × 9² × 30
V = 810·π cm³
Volume of the hemisphere = (4/3) × π × r³/2
r = 9 cm
Therefore; Volume of the hemisphere = (4/3) × π × 9³/2
(4/3) × π × 9³/2 = 486·π
Volume of the hemisphere = 486·π cm³
Volume of the composite figure = (810 + 486)·π cm³
Volume of the composite figure = 1296·π cm³
The total volume of the shape = k·π cm³
Therefore; k·π = 1296·π
k = 1296