Question

Use the image to answer the 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
[]

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:

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