2. A company makes cereal boxes with a volume of \( 432 \frac{1}{4} \) cubic inches. The dimensions of one of the cereal boxes is shown. What is the width of the box? A. How can you find the volume of the cereal box? B. Complete the equation to find the volume of the cereal box. \( V=2 \times a \times b \) \( 432 \frac{1}{4}=\square \times w \times \square \) \( \frac{1729}{4}=\frac{\square}{\square} \times w \times \frac{\square}{1} \) \( \frac{1729}{4}=\frac{\square}{2} w \) \( w=\frac{\square}{\square} \times \frac{\square}{\square} \) 14in C. What is the width of the cereal box? Turn and Talk in Task 2 , if the width was given and the length was not, would the steps you used to find the length be different than the steps you used to find the width? Explain.

To solve the problem, let's break it down step by step. ### A. How can you find the volume of the cereal box? The volume \( V \) of a rectangular box can be calculated using the formula: \[ V = l \times w \times h \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the box. ### B. Complete the equation to find the volume of the cereal box. We are given that the volume of the cereal box is \( 432 \frac{1}{4} \) cubic inches. First, let's convert this mixed number into an improper fraction: \[ 432 \frac{1}{4} = \frac{432 \times 4 + 1}{4} = \frac{1728 + 1}{4} = \frac{1729}{4} \] Now, we can complete the equation: \[ V = 2 \times a \times b \] Assuming \( a \) and \( b \) are the dimensions of the base of the box, we can express the volume as: \[ \frac{1729}{4} = 2 \times w \times h \] This implies: \[ \frac{1729}{4} = \frac{2}{1} \times w \times \frac{h}{1} \] Now, we can simplify this to: \[ \frac{1729}{4} = \frac{2h}{1} \times w \] ### C. What is the width of the cereal box? To find the width \( w \), we can rearrange the equation: \[ w = \frac{\frac{1729}{4}}{\frac{2h}{1}} = \frac{1729}{4} \times \frac{1}{2h} = \frac{1729}{8h} \] Now, we need to know the height \( h \) to calculate \( w \). If we assume \( h = 14 \) inches (as mentioned in the problem), we can substitute this value into the equation: \[ w = \frac{1729}{8 \times 14} \] Now, let's calculate \( w \): \[ w = \frac{1729}{112} \] Now, we will perform the calculation to find the width \( w \). Calculate the value by following steps: - step0: Calculate: \(\frac{1729}{112}\) - step1: Reduce the fraction: \(\frac{247}{16}\) The width \( w \) of the cereal box is calculated to be: \[ w = \frac{1729}{112} = 15 \frac{7}{16} \text{ inches} \quad \text{or} \quad 15.4375 \text{ inches} \] ### Conclusion - The width of the cereal box is \( 15 \frac{7}{16} \) inches. ### Discussion on the Steps If the width was given and the length was not, the steps to find the length would be similar. You would still use the volume formula \( V = l \times w \times h \) and rearrange it to solve for \( l \): \[ l = \frac{V}{w \times h} \] The process of rearranging the formula and substituting known values would remain consistent, regardless of which dimension is unknown.