A box has 3 sections. 2 sections have the same measurements, but the 3rd is 2/3rd the volume of one of the sections. If they all have the same height and width, how long is section 3?

Question

A recycling bin that has a length of 3 feet, a width of 2 feet, and a height of 2 feet has three separate sections inside for sorting. Sections 1 and 2 have identical measurements but section 3 has 2/3 the volume of section 1 or 2. If all three sections have the same height and width, how long is section 3?

Answer 1

Let Vt = total volume of the container, Vt = 2 x 2 x3 = 12

The volume of bin1 or bin2 = L x 4, where L is the length of either bin1 or bin2

The volume of bin3 is 2/3 x L x 4.

The total volume is the sum of each bin, so 12 = 2 x (L x 4) + 2/3 x L x 4.

Solving for L = 8L + 8/3L = 12 or L = 1.125 ft

The total length is 3 ft, so the length of bin3 is 3 - 2 x 1.125 = 0.75 ft.

You can check by using the results to show that the volume of bin3 is 2/3 the volume of bin1 or bin2.