Final answer:
To find the amount of cardboard needed to make the box, calculate its surface area by adding the areas of all its six faces. In this case, it would be needed around 4000 square centimeters of cardboard.
Step-by-step explanation:
To find the amount of cardboard needed to make the box, we need to calculate its surface area. The surface area of a box is found by adding the areas of all its six faces. In this case, the box has three pairs of faces that are congruent, so we can simplify the calculation.
The surface area is equal to twice the area of one pair of congruent faces, plus four times the area of one of the remaining faces. Using the dimensions given, we can calculate the surface area as follows:
- Calculate the area of one pair of congruent faces: 2(length * width) = 2(30cm * 20cm) = 1200cm².
- Calculate the area of one of the remaining faces: width * height = 20cm * 20cm = 400cm².
- Calculate the total surface area: 2 * 1200cm² + 4 * 400cm² = 2400cm² + 1600cm² = 4000cm².
Therefore, it would be needed approximately 4000 square centimeters of cardboard to make the box.