Question 152016
Answer: 20% of surface area of each is not painted
</pre><font size=4><b>Proof:</pre>
Before it was cut into half, all the sides are equal right? (a cube is a square with 3-D body). Then it was cut to half and became a rectangular solid. One side of which is not painted.
We have to remember {{{Surface Area}}} of a rectangular solid:
{{{SA=2LH+2LW+2WH}}} ---------------------> EQN 1
Important: before it has ALL SIDES EQUAL, and when cut into half there appears now the {{{Length}}} and the {{{Width}}}----> the dimensions of the {{{Width}}} now will be half of the {{{Length}}}: {{{W=(1/2)L}}}, Also the {{{Height}}} remains the same as the {{{Length}}}. Only the {{{Width}}} changed when cut into half.
For the {{{Area}}} of the new rectangular solid, since one side is NOT painted, {{{SA[new]=2LH+1LW+2WH}}} -------------------> EQN 2
NOW, IF YOU PLUG IN VALUES IN EQN 1 AND EQN 2, REMEMBER {{{L=H}}}, {{{W=(1/2)
L}}} and make {{{(EQN2/EQN)-1)}}}. Get ABSOLUTE VALUE (no negative)*100% ----------> PERCENTAGE of Surface Area NOT painted.
Hope this helps.
Thank you,
Jojo