Two spherical bodies made of the same material have radii of \(0.2~ \text m\) and \(0.8~ \text m,\) and absolute temperatures of \(800 ~ \text K \) and \(400~ \text K\) respectively. Assuming the effect of the surroundings is negligible, if the smaller body radiates energy \(E, \) in a given time, how much energy does the larger body radiate in the same time?
1. \(256 E\)
2. \(16E\)
3. \(64E\)
4. \(E\)