To find the width of the box, we can use the formula for the volume of a right rectangular prism, which is given by:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
We know the volume is 162,000 cubic centimeters, the length is 90 cm, and the height is 40 cm. We can rearrange the formula to solve for the width:
\[ \text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} \]
Plugging in the values:
\[ \text{Width} = \frac{162,000}{90 \times 40} \]
Now calculate the denominator:
\[ 90 \times 40 = 3600 \]
Now substitute this back into the equation for width:
\[ \text{Width} = \frac{162,000}{3600} \]
Now, perform the division:
\[ \text{Width} = 45 \]
Therefore, the width of the box is 45 cm.