Answer: To find the lateral area of a cube, we need to know the length of one of its sides. The formula for the volume of a cube is V = a³, where V is the volume and a is the length of one side. We are given that the volume of the cube is 216 cm³. Therefore, we can solve for a as follows:
a³ = 216 cm³
a = ∛216 cm
a = 6 cm
The length of one side of the cube is 6 cm. The formula for the lateral area of a cube is L = 4a², where L is the lateral area and a is the length of one side. Substituting a = 6 cm, we get:
L = 4(6 cm)²
L = 144 cm²
Therefore, the lateral area of the cube whose volume is 216 cm³ is 144 cm.