Question

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 15%, the height has been increased by 25%, 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.

Answer 1

Let's assume that the regular box has dimensions of length L, height H, and width W, and the family value box has dimensions of length 1.15L (since the length has increased by 15%), height 1.25H (since the height has increased by 25%), and width W (since it remains the same).

The volume of the regular box is V_regular = LHW, and the volume of the family value box is V_value = 1.15L * 1.25H * W = 1.4375LHW.

To find the percentage increase in volume, we can calculate the difference between the two volumes, divide by the regular box volume, and then multiply by 100 to get a percentage:

percentage increase = [(V_value - V_regular)/V_regular] * 100
= [(1.4375LHW - LHW)/LHW] * 100
= 43.75%

Therefore, the volume of the family value box is approximately 43.75% larger than the regular box. Rounded to the nearest percent, the answer is 44%.