# Energy Radiating Off of a Cube Split Into Two Pieces

This is somewhat a Physics question, but ends of being more of an algebra/geometry-related question.

Anyway, there is a cube that radiates with a power $P_0$ and it is "cut" into two pieces. These two pieces radiate energy with a power of $P_1$. Find the ratio of $P_1$/$P_0$.

Heat transfer for radiation is defined as P = $\delta$Q/$\delta$T = e $\sigma$ A $T^4$

Everything is constant between the two cubes (except for their total surface area, obviously)

The ratio ends up being $P_1$/$P_0$ = $A_1$/$A_0$

My problem is that it doesn't given any details about the size before or after the cube is cut. I tried every geometric comparison I could think of, I always ended up with 1/2 or 2. The answer supplied is 4/3. Any hints?

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I kind of makes sense that $P_1 > P_0$ such that the ratio is large than 1. Don't you think? –  Fabian Apr 26 '12 at 5:05
What is $P$? What is $\delta$? What is $Q$? What is $T$? What is e? What is $\sigma$? What is $A$? Don't worry, I know what 4 is. –  Gerry Myerson Apr 26 '12 at 5:54
@Gerry, I only know $T$ is temperature but all that matters is the ratio of areas since everything else is constant. –  Dan Brumleve Apr 26 '12 at 5:58
The answer is only correct when the cube is cut into "boxes." If you slice down along a diagonal of one of the faces, the ratio is $5:3$. And there are many other possibilities for cutting. Some, like cutting off a tiny corner, make no appreciable difference. –  André Nicolas Apr 26 '12 at 6:21