Question

A solid cylinder of length l and radius r is heat upto same temperature as that of a cube of edge

Answer 1

your question is incomplete . A complete question is ------> A solid cylinder of length l and radius r is heat up to same temperature as that of cube of edge length a.If both have same material,volume and allowed to cool under similar condition,ratio of amount of radiation radiated will be ?

amount of radiation radiated , dQ/dt = $\sigma AT^4$

so, ratio of radiation = $\frac{\sigma_1A_1T_1^4}{\sigma_2A_2T_2^4}$

as temperature remains constant and material used to form cylinder and cube are also same.
so, $T_1=T_2$. and $\sigma_1=\sigma_2$

area of cylinder, $A_1$ = 2πrl
area of cube , $A_2$ = 6a²

a/c to question,
volume of cylinder = volume of cube
πr²l = a³
l = a³/πr²

now, ratio of radiation radiated = $\frac{2\cancel{\pi}\cancel{r}\frac{\cancel{a^2}.a}{\cancel{\pi}\cancel{r}.r}}{6\cancel{a^2}}$

= $\frac{a}{3r}$