Calculate Cuboid Volume: 12cm Base Perimeter, 8cm Height Problem

To solve this problem, we'll follow these steps:

• Step 1: Calculate the side length of the square base.
• Step 2: Calculate the area of the square base.
• Step 3: Compute the volume of the cuboid using the area and height.

Let's work through each step:

Step 1: The perimeter of the square base is given as 12 cm. We can find the side length $s$ of the square using the perimeter formula:

$P = 4s$

So,

$12 = 4s$ which implies $s = \frac{12}{4} = 3 \text{ cm}$.

Step 2: The area of the square base is then:

$\text{Area} = s^2 = 3^2 = 9 \text{ cm}^2$.

Step 3: To find the volume of the cuboid, we use the formula for volume:

$V = \text{Base Area} \times \text{Height} = 9 \times 8 = 72 \text{ cm}^3$.

Thus, we have successfully determined that it is possible to calculate the volume of the cuboid, and the volume is $72 \text{ cm}^3$.

Therefore, the correct answer to the problem is Yes.