\(\because\) 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

\(\frac{R_{\text {cylinder }}}{R_{\text {cube }}}=\frac{a}{3 r}\)