A small rectangular solid with dimensions of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash$times $0\mathrm{.}65\backslash$mathrm$\{$~m$\}\backslash$times $0\mathrm{.}65\backslash$mathrm$\{$~m$\}\backslash )$ as shown in Figure $4$

heeds to be needs to be heated inside a relatively large oven with walls and the air at $\backslash (1\mathrm{.}57^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

Figure $4$: A rectangular solid with specified dimensions

The solid emissivity is estimated to be $0\mathrm{.}83,$ and its surface temperature is $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The solid moves continuously through the large oven on an open chain belt conveyor. Neglect the natural convection heat transfer.

$($a$)$ Calculate the total surface area of the cube.

$($b$)$ calculate the radiation heat transfer rate to the solid.