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.
By what percentage does the volume of the box increase from the regular box to the value box? Round your answer to the nearest percent.

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 \(\boxed{44\%}\).