Question

The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? the length is 6in. width is 5/6 and the height is 1 2/6 the cube side is 1/6

Answer 1

The volume of the prism = 6 * 5/6 * 8/6  =   240/36   in^3

No. of cube  = 240 / 36  / 1/6
                    = 240 * 6 / 36
                    = 240 / 6
                    = 40 

Answer 2

The number of cubes should be 1.440.

• The calculation is as follows:

Calculate the volume of each shape is as follows:

Volume of rectangle = $6 \times 5\div 6 \times 1\ 2\div 6 = 6\ 2\div 3$ cubic inches.

And,

Volume of cube =$1\div6 \times 1\div6 \times 1\div6 = 1\div216$ cubic inch.

Now

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

So,

$= (6\ 2\div 3) \div (1\div 216)$

= 1.440

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