Step 1 :A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length of the box has been increased by 25%, the height has been increased by 15%, and the width remains the same.
Step 2 :The volume of a box is given by the formula \(V = l \times w \times h\) where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
Step 3 :If the length is increased by 25% and the height is increased by 15%, the new volume \(V'\) is given by \(V' = 1.25l \times w \times 1.15h = 1.4375V\).
Step 4 :The percentage increase in volume is then given by \(\frac{V' - V}{V} \times 100 \%\).
Step 5 :Final Answer: The volume of the box increases by approximately \(\boxed{44\%}\).