Sample Problem

The length of the following box is 36 cm. If we cut the length into 3 parts as shown, the surface area will increase by 120 cm2. What is the volume of this box?


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When we cut the cube into 3 parts, we make 2 cuts, thus revealing 4 cross sections. These 4 cross sections are a total of 120 cm2. Therefore, each cross section has an area of 120 ÷ 4 = 30. Since the base area is 30, the volume of the box is 30 × 36 = 1080 cm3.