Calculate Rectangular Prism Volume: Given Surface Area 240 cm² and Height 3

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula to find the unknown dimension
• Step 3: Calculate the volume using the known dimensions

Now, let's work through each step:
Step 1: We know the surface area $S = 240 \, \text{cm}^2$, and two dimensions: 12 cm and 3 cm.

Step 2: The formula for the surface area of a rectangular prism is:
$S = 2(lw + lh + wh)$
Substituting the known values into the equation:
$240 = 2(12 \times 3 + 12 \times h + 3 \times h)$

Simplify and solve for $h$:
$240 = 2(36 + 12h + 3h)$
$240 = 2(36 + 15h)$
$240 = 72 + 30h$
$168 = 30h$
$h = \frac{168}{30} = 5.6 \, \text{cm}$

Step 3: Now that we know all dimensions, use the volume formula:
$V = l \times w \times h = 12 \times 3 \times 5.6$

Perform the calculation:
$V = 36 \times 5.6 = 201.6 \, \text{cm}^3$

Therefore, the volume of the rectangular prism is $201.6 \, \text{cm}^3$.