Calculate Cuboid Volume: 5cm × 4cm with 94cm² Surface Area

To solve this problem, we are going to determine the volume of a cuboid given its length, width, and overall surface area. Here's how we will do it:

• Firstly, calculate the height $h$ of the cuboid using the surface area formula.
• Then, use the calculated height to determine the volume of the cuboid.

Now, let's work through each step:

Step 1: Calculate the height $h$.

We know the surface area of a cuboid is given by the formula:

$2(lw + lh + wh) = \text{Surface Area}$

Substituting the known values:

$2(5 \cdot 4 + 5 \cdot h + 4 \cdot h) = 94$

Simplify:

$2(20 + 5h + 4h) = 94$ $2(20 + 9h) = 94$

Divide both sides by 2:

$20 + 9h = 47$

Simplify further to solve for $h$:

$9h = 27$ $h = 3 \, \text{cm}$

Step 2: Calculate the volume using the height $h$.

Now that we know $h = 3 \, \text{cm}$, use the volume formula for the cuboid:

$\text{Volume} = l \times w \times h$ $\text{Volume} = 5 \times 4 \times 3 = 60 \, \text{cm}^3$

Therefore, the volume of the cuboid is $\mathbf{60 \, \text{cm}^3}$.