To find the width of the box, we can use the formula for the volume \( V \) of a right rectangular prism, which is given by:
\[ V = \text{length} \times \text{width} \times \text{height} \]
We know the following values:
- Volume \( V = 162,000 \) cubic centimeters
- Height \( h = 40 \) centimeters
- Length \( l = 90 \) centimeters
We can rearrange the formula to solve for width \( w \):
\[ w = \frac{V}{l \times h} \]
Now, substituting in the known values:
\[ w = \frac{162,000}{90 \times 40} \]
Calculating the denominator:
\[ 90 \times 40 = 3600 \]
Now substituting this back into the equation for width:
\[ w = \frac{162,000}{3600} \]
Calculating the width:
\[ w = 45 , \text{cm} \]
Therefore, the width of the box is 45 cm.