The image shows a rectangular box with the dimensions labeled: 5 cm, 15 cm, and 30 cm. The question asks to calculate the surface area of the box in square centimeters.

To calculate the surface area $A$ of a rectangular box, the formula is:

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

Where:

• $l$ is the length (15 cm),
• $w$ is the width (5 cm),
• $h$ is the height (30 cm).

Let's calculate it:

$A = 2(15 \times 5) + 2(15 \times 30) + 2(5 \times 30)$

I'll compute this now.The surface area of the rectangular box is $1350 \, \text{cm}^2$.

Would you like more details or have any questions?

Here are five related questions to expand on this concept:

1. How do you calculate the surface area of a cube?
2. What is the difference between surface area and volume?
3. Can the surface area formula be applied to other shapes, such as cylinders or spheres?
4. How does changing one dimension affect the surface area of a rectangular box?
5. How can surface area be useful in real-world applications like packaging?

Tip: When working with 3D shapes, always double-check if you are calculating for volume or surface area, as they are related but distinct.