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A rectangular prism 3cm by 5cm by 6cm is painted mauve and is then cut into 1 cm cubes what is the total unpainted surface area of these cubes

 Feb 11, 2018
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3 * 5 * 6

 

There are a total of  90 cubes

 

The unpainted ones will be the ones in the middle of the prism

 

Let 3 be the height

 

There will be 2 * 6 * 5  =  60  painted cubes on the top and bottom

 

There will  2 * 6  +   2 * 3  =  18 more painted cubes "sandwiched" between the top and bottom surfaces

 

So...the total unpainted cubes  is  90  - 78   =   12

 

So their total surface area is just   [12 * 6 ] cm^2   =  72 cm^2

 

P.S.  -  I believe there is also a "formula" for this....we are cutting away 2 inches in every dimension...so  (3 - 2) (5 - 2) (6 - 2)  =  1 * 3 * 4    =   12 cubes

 

 

cool cool cool

 Feb 11, 2018
edited by CPhill  Feb 11, 2018

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