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

Hans007
Feb 11, 2018

#1**+1 **

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

CPhill
Feb 11, 2018