To determine 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 height is 40 cm, and the length is 90 cm. We can substitute these values into the formula:
\[ 162,000 = 90 \times \text{Width} \times 40 \]
Now, we can simplify the equation:
\[ 162,000 = 3,600 \times \text{Width} \]
Next, we solve for the width:
\[ \text{Width} = \frac{162,000}{3,600} \]
Calculating that:
\[ \text{Width} = 45 \text{ cm} \]
Thus, the width of the box is 45 cm.
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