To find the width of the box, we can use the formula for the volume of a rectangular prism, which is:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given that the volume is 162,000 cubic centimeters, the height is 40 cm, and the length is 90 cm, we can set up the equation:
\[ 162,000 = 90 \times \text{width} \times 40 \]
Now, we can simplify the equation. First, multiply the length and height:
\[ 90 \times 40 = 3600 \]
Then, substitute back into the volume equation:
\[ 162,000 = 3600 \times \text{width} \]
Now, solve for width by dividing both sides by 3600:
\[ \text{width} = \frac{162,000}{3600} \]
Calculating this gives us:
\[ \text{width} = 45 \]
Therefore, the width of the box is 45 cm.