math genius....i need help!!?

Question

i found this question from a SAT book, and i couldn't figure it out. so hope u guys and help me! thx a lot

A wooden block is in the shape of a rectangular prism with dimensions n cm, (n+3) cm, and (n+9)cm, for some integer n. The surface of the block is painted and the block is then cut into 1 cm cubes by cuts parallel to the faces. if exactly half of the cubes have no paint on them, find the dimensions of the original block.

Answer 1

First find the surface area...

2(n*(n+3))+2[(n+3)*(n+9)]+
2[n*(n+9)]=

6n^2+48n+54 (1)

So to find the number of blocks...

n*(n+3)*(n+9)=n^3+12n^2+27n (2)

Then the surface area formula (1) equals half of the number of blocks (2). So set (1) equal to .5 times (2) and solve for n.

I hope this helps!!