Math CentralQuandaries & Queries


Question from Chantel, a student:

The length, width and height of a cubical shipping container are all decreased by 1.0 ft, thereby decreasing the volume of the cube by 37 ft3(feet-cubed) What was the volume of the original container? (recall: volume of cube with a side length x=x3) Define the variable, write a quadratic equation and solve by factoring.

Hi Chantel,

Suppose the length of each side of the cube is $x$ feet. What is the volume of the cube?

If each side length is decreased by 1 foot what are the new side lengths? What is the volume of this smaller cube?

The volume of the smaller cube is 37 cubic feet smaller than the volume of the original cube. This gives you an equation in the variable $x.$ Solve for $x.$


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