Final answer:
The lateral surface area of a cube with side length 9 cm is 324 cm². It's calculated by multiplying the perimeter of one side (4 × 9 cm) by the side length (9 cm).
Step-by-step explanation:
The lateral surface area of a cube is calculated by multiplying the perimeter of one base by the cube's height. Since a cube has all sides of equal length, you can think of the height as just another side length. For a cube with a side length of 9 cm, the calculation is as follows:
Lateral Surface Area = Perimeter of the base × Height
Lateral Surface Area = 4 × side × side = 4 × 9 cm × 9 cm
Lateral Surface Area = 36 cm × 9 cm
Lateral Surface Area = 324 cm²
This is because there are four sides of the cube that make up the lateral surface area, and each side is a square. Therefore, the total lateral surface area is the sum of the areas of these four sides.