Question

a cube has an edge length of 9 centimeters. if the side length is increased by a factor of 3, how much larger is the perimeter of a face of the new cube? 72 cm 72 cm² 108 cm 108 cm²

Explanation:

Step1: Find the new side - length

The original side - length $a = 9$ cm. If it is increased by a factor of 3, the new side - length $A=9\times3 = 27$ cm.

Step2: Calculate the perimeter of a face of the original cube

The perimeter of a face of a cube with side - length $a$ is $P_1 = 4a$. For $a = 9$ cm, $P_1=4\times9=36$ cm.

Step3: Calculate the perimeter of a face of the new cube

The perimeter of a face of a cube with side - length $A$ is $P_2 = 4A$. For $A = 27$ cm, $P_2=4\times27 = 108$ cm.

Step4: Find the difference in perimeters

The difference $\Delta P=P_2 - P_1$. So, $\Delta P=108 - 36=72$ cm.

Answer:

72 cm