To find the width of the box, we can use the formula for the volume of a right rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
We know the volume (162,000 cm³), the height (40 cm), and the length (90 cm). We can rearrange the formula to solve for width:
\[ \text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} \]
Now, substituting the known values into the formula:
\[ \text{Width} = \frac{162,000 \text{ cm}^3}{90 \text{ cm} \times 40 \text{ cm}} \]
Calculating the denominator:
\[ 90 \text{ cm} \times 40 \text{ cm} = 3600 \text{ cm}^2 \]
Now, substituting that back into the equation for width:
\[ \text{Width} = \frac{162,000 \text{ cm}^3}{3600 \text{ cm}^2} = 45 \text{ cm} \]
Therefore, the width of the box is 45 cm.