Use the image to answer the question.

Question

An illustration shows a 3 D cuboid with length, width, and height marked as 5 centimeters. The edges that are not visible are marked as dashed lines.

Manny created a storage bin for the family to hold the remote control and cell phone cords. What is the total surface area of the storage bin?

(1 point)
surface area=

cm2
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Answer 1

To calculate the total surface area of a cuboid, we use the formula:

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

where:

• \( l \) is the length,
• \( w \) is the width,
• \( h \) is the height.

Given that the length \( l \), width \( w \), and height \( h \) are all 5 cm, we can substitute these values into the formula:

1. Calculate \( lw \): \[ lw = 5 , \text{cm} \times 5 , \text{cm} = 25 , \text{cm}^2 \]

2. Calculate \( lh \): \[ lh = 5 , \text{cm} \times 5 , \text{cm} = 25 , \text{cm}^2 \]

3. Calculate \( wh \): \[ wh = 5 , \text{cm} \times 5 , \text{cm} = 25 , \text{cm}^2 \]

4. Now, add those results: \[ lw + lh + wh = 25 , \text{cm}^2 + 25 , \text{cm}^2 + 25 , \text{cm}^2 = 75 , \text{cm}^2 \]

5. Finally, multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times 75 , \text{cm}^2 = 150 , \text{cm}^2 \]

Thus, the total surface area of the storage bin is:

\[ \text{Surface Area} = 150 , \text{cm}^2 \]

So, the answer is:

\[ \text{surface area} = 150 , \text{cm}^2 \]