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22 August, 14:20

The figure below shows a rectangular prism and a cube: A rectangular prism and a cube are drawn side by side. The length of the rectangle prism is 6 inches, the width is 5 over 6 inch, and its height is 1 and 2 over 6 inches. The cube has a side length of 1 over 6 inch. How many such cubes are required to completely pack the prism without any gap or overlap?

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  1. 22 August, 14:42
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    Calculate the volume of each shape.

    Volume of rectangle = 6 x 5/6 x 1 2/6 = 6 2/3 cubic inches.

    Volume of cube = 1/6 x 1/6 x 1/6 = 1/216 cubic inch.

    Now divide the volume of the rectangle by the volume of the cube:

    6 2/3 / 1/216 = 1440

    It will take 1.440 cubes to fill the rectangle.
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