+110 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
+128475 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
