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You want to construct an open-top box that is 6 inches deep, with a square base. It must have a volume of 864 cubic inches. You have one big piece of cardboard. You will start by cutting it down to a square, and then you will cut smaller squares out of each corner and fold up the sides.

You want to construct an opentop box that is 6 inches deep with a square base It must have a volume of 864 cubic inches You have one big piece of cardboard You class=

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The statements that are true are the volume of the box is v = lwh = 864 in³ and the volume can be expressed in an equation as v = 6x² = 864in³

Volume of a Square

The volume of a square box is equal to the cube of the length of the side of the square box. The formula for the volume is V = l³, where "l" is the length of the side of the square box.

In the given problem, the volume of the box is 864 cubic inches.

However, we have to remember that the box isn't a square, but rather the base has a square shape.

The volume of the figure is

v = l * w * h

  • l = length
  • w = width
  • h = height

If we divide the volume by the height, we will have the area of the figure

Area = volume / height

Area = 864 / 6

Area = 144 square inches

Since the base has a square shape;

A = l²

144 = l²

l = √144

l = 12 in

The side length is 12 inches.

Learn more on volume of square here;

https://brainly.com/question/22789685

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