A solid cylinder of length $L$ and radius $r$ is heat upto same temperature as that of a cube of edge length $a$. If both have same material, volume and allowed to cool under similar conditions, then ratio of amount of radiations radiated will be (Neglect radiation emitted from flat surfaces of the cylinder)
Medium
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(a)
$\because$ Both have same volume
$\therefore a^3=\pi r^2 L \quad \dots (1)$
Amount of radiation $\propto$ Surface area [ $\because$ Temperature, material are same for both]
[ $\because$ Temperature, material are same for both]
$\frac{\text { Radiation cylinder }}{\text { Radiation cube }}=\frac{2 \pi r L}{6 a^2}=\frac{2 \pi r L \cdot a}{6 a^3}$
using equation $(1)$
We get
$\frac{R_{\text {cylinder }}}{R_{\text {cube }}}=\frac{a}{3 r}$
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