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 are given the following information:
- Volume = 162,000 cubic centimeters
- Height = 40 cm
- Length = 90 cm
We can rearrange the formula to find the width:
\[ \text{width} = \frac{\text{Volume}}{\text{length} \times \text{height}} \]
Substituting in the known values:
\[ \text{width} = \frac{162,000 , \text{cm}^3}{90 , \text{cm} \times 40 , \text{cm}} \]
Calculating the denominator:
\[ 90 , \text{cm} \times 40 , \text{cm} = 3600 , \text{cm}^2 \]
Now we can calculate the width:
\[ \text{width} = \frac{162,000 , \text{cm}^3}{3600 , \text{cm}^2} \]
Calculating this gives:
\[ \text{width} = 45 , \text{cm} \]
So, the width of the box is 45 cm.