Question

a cuboid has a volume of (108\text{ cm}^3)
the length of the cuboid is (6\text{ cm}) and the height is (9\text{ cm}).

calculate the surface area of the cuboid.

Explanation:

🆕 New Concept Discovered: Surface Area of Cuboids
Total area of all six outer faces

Step 1: Find the width of the cuboid

The volume \( V \) of a cuboid is calculated using the formula:

$$ V = \text{length} \times \text{width} \times \text{height} $$

Given:

• \( V = 108\text{ cm}^3 \)
• \( \text{length } (l) = 6\text{ cm} \)
• \( \text{height } (h) = 9\text{ cm} \)

Let \( w \) represent the width:

$$ 108 = 6 \times w \times 9 $$

$$ 108 = 54 \times w $$

$$ w = \frac{108}{54} = 2\text{ cm} $$

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Step 2: Calculate the surface area

A cuboid has 6 rectangular faces. The total surface area (\( A \)) is the sum of the areas of all these faces:

$$ A = 2(lw + lh + wh) $$

Substitute the values \( l = 6 \), \( w = 2 \), and \( h = 9 \):

$$ A = 2((6 \times 2) + (6 \times 9) + (2 \times 9)) $$

$$ A = 2(12 + 54 + 18) $$

$$ A = 2(84) $$

$$ A = 168\text{ cm}^2 $$

Answer:

\( 168\text{ cm}^2 \)