To find the width of a cereal box with these given dimensions and volume, we need to use the formula for the volume of a rectangular prism. The formula for the volume [tex]\( V \)[/tex] of a rectangular prism is:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
We are given the following values:
- Volume [tex]\( V = 1725 \)[/tex] cm³
- Length [tex]\( L = 25 \)[/tex] cm
- Height [tex]\( H = 23 \)[/tex] cm
We can rearrange the formula to solve for the width [tex]\( W \)[/tex]:
[tex]\[ W = \frac{V}{L \times H} \][/tex]
Next, we substitute the given values into the equation:
[tex]\[ W = \frac{1725 \, \text{cm}^3}{25 \, \text{cm} \times 23 \, \text{cm}} \][/tex]
First, calculate the product of the length and height:
[tex]\[ 25 \, \text{cm} \times 23 \, \text{cm} = 575 \, \text{cm}^2 \][/tex]
Then, divide the volume by this product to find the width:
[tex]\[ W = \frac{1725 \, \text{cm}^3}{575 \, \text{cm}^2} \][/tex]
Now, perform the division:
[tex]\[ W = 3 \, \text{cm} \][/tex]
Therefore, the width of the cereal box is [tex]\( 3 \)[/tex] cm.
