Calculate Cuboid Volume: Surface Area 136 cm³ with 8 cm Length Problem

To solve this problem, follow these steps:

• Step 1: Identify the given information: $l = 8 \, \text{cm}$, $w = 4 \, \text{cm}$, and $S = 136 \, \text{cm}^2$.
• Step 2: Use the surface area formula to find height $h$: $136 = 2(8 \cdot 4 + 8 \cdot h + 4 \cdot h)$.
• Step 3: Simplify and solve for $h$.
• Step 4: Use the volume formula $V = l \cdot w \cdot h$.
• Step 5: Substitute the value of $h$ into the volume formula.
• Step 6: Calculate and obtain the final result.

Now, let's calculate:

Starting with the surface area equation:

$136 = 2(8 \cdot 4 + 8 \cdot h + 4 \cdot h)$.

Simplifying gives:

$136 = 2(32 + 8h + 4h)$.

$136 = 2(32 + 12h)$.

$136 = 64 + 24h$.

Subtract 64 from both sides:

$72 = 24h$.

Divide both sides by 24:

$h = 3 \, \text{cm}$.

Now, calculate the volume using $V = l \cdot w \cdot h$:

$V = 8 \cdot 4 \cdot 3$.

$V = 96 \, \text{cm}^3$.

Therefore, the volume of the cuboid is $96 \, \text{cm}^3$.