Consider a truncated cone with faces of radii $R_1$ and $R_2$ and length $L,$ as shown in Fig. $1.$ If the temperatures on the faces are $T_C$ and $T_m,$ respectively, and if insulation prevents heat loss out the sides, show that the conduction rate is given by

$\frac{dQ}{dt}=k{R}_1{R}_2\frac{T_H-T_C}{L}$