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A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 2-inch cubes as possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?

 Nov 24, 2020
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To make things easy, let  the box  length = 6  and the   box width =10  and the box  height  = 5

 

We can put 3 cubes along the length  and 5 cubes along the width.....thus....each layer of cubes contains 3 x 5 =  15 cubes

 

And we  can  stack  2  layers of cubes  =  2x15 = 30 cubes in total

 

The volume  of  the box is  6 * 5 * 10 =  300 in^3

 

The volume of the  cubes =  2^3 * 30  = 240 in^2

 

% of box volume taken up  by the  cubes  =  240 / 300  =  8/10  = 80%

 

 

cool cool cool

 Nov 24, 2020

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