Ratio of volume

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 25%

, the height has been increased by 30%

, 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

The formula for the volume of a box is length • width • height. Let's call the volume of the regular size V₁=Lwh.

For the family size box, the length is 125% of the original. As a decimal, 125%=1.25. so L₂=1.25L. Likewise, the height of the family value box is 130% of the original, or h₂=1.3h. The new volume, V₂=1.3h •1.25L •w. Multiplying the coefficients gives V₂= 1.625Lwh. Note the 1.625 coefficient in the second volume compared to the "understood coefficient" of 1 from the first volume. The second box is .625 bigger, which is 62.5%, or, rounded up, about 63%.

I hope this helps!

Have fun mathing, and reach out if you need help!

Liz Z.