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?
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?
Answers
GPT-4o mini
To find the total surface area of a cuboid (or rectangular prism), the formula is:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
In this case, the dimensions of the cuboid (length, width, and height) are all given as 5 centimeters:
- \( l = 5 \, \text{cm} \)
- \( w = 5 \, \text{cm} \)
- \( h = 5 \, \text{cm} \)
Now, we can substitute these values into the formula:
\[
\text{Surface Area} = 2(5 \times 5 + 5 \times 5 + 5 \times 5)
\]
Calculating the individual area components:
\[
5 \times 5 = 25
\]
Therefore, the equation becomes:
\[
\text{Surface Area} = 2(25 + 25 + 25)
\]
Combining the terms:
\[
\text{Surface Area} = 2(75) = 150
\]
Thus, the total surface area of the storage bin is
\[
\boxed{150 \, \text{cm}^2}
\]
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
In this case, the dimensions of the cuboid (length, width, and height) are all given as 5 centimeters:
- \( l = 5 \, \text{cm} \)
- \( w = 5 \, \text{cm} \)
- \( h = 5 \, \text{cm} \)
Now, we can substitute these values into the formula:
\[
\text{Surface Area} = 2(5 \times 5 + 5 \times 5 + 5 \times 5)
\]
Calculating the individual area components:
\[
5 \times 5 = 25
\]
Therefore, the equation becomes:
\[
\text{Surface Area} = 2(25 + 25 + 25)
\]
Combining the terms:
\[
\text{Surface Area} = 2(75) = 150
\]
Thus, the total surface area of the storage bin is
\[
\boxed{150 \, \text{cm}^2}
\]