Solution:

We are tasked with calculating the surface area of a cuboid after converting the given dimensions from meters (m) into centimeters (cm). Let’s proceed step by step:

Step 1: Convert the dimensions to centimeters.

Since $1 \, \text{m} = 100 \, \text{cm}$, we multiply each dimension by $100$:

• Length $= 20 \, \text{m} = 20 \times 100 = 2000 \, \text{cm}$
• Width $= 13 \, \text{m} = 13 \times 100 = 1300 \, \text{cm}$
• Height $= 8 \, \text{m} = 8 \times 100 = 800 \, \text{cm}$

Step 2: Calculate the surface area of the cuboid.

The formula for the surface area of a cuboid is:

$\text{Surface Area} = 2 \times \left( lw + lh + wh \right)$ Where $l$ is the length, $w$ is the width, and $h$ is the height.

Substitute the values $l = 2000 \, \text{cm}$, $w = 1300 \, \text{cm}$, and $h = 800 \, \text{cm}$:

$\text{Surface Area} = 2 \times \left( (2000 \times 1300) + (2000 \times 800) + (1300 \times 800) \right)$

Step 3: Perform the calculations.

1. $2000 \times 1300 = 2,600,000$
2. $2000 \times 800 = 1,600,000$
3. $1300 \times 800 = 1,040,000$

Now add these results:

$2,600,000 + 1,600,000 + 1,040,000 = 5,240,000$

Multiply by $2$:

$\text{Surface Area} = 2 \times 5,240,000 = 10,480,000 \, \text{cm}^2$

Final Answer:

The surface area of the cuboid is 10,480,000 cm².

Would you like a breakdown of how each step was solved or additional examples?

Related Questions:

1. How do you convert cubic meters into cubic centimeters?
2. What is the formula for the volume of a cuboid?
3. How would the surface area change if the height was doubled?
4. If all dimensions were halved, what would be the new surface area?
5. How do you calculate the diagonal of a cuboid?

Tip:

Always double-check unit conversions in problems involving area and volume to avoid mistakes!