(i) Hemispherical shape of radius R

(ii) Two concentric cylinders

i)for shape factor of hemispherical shape of radius R We have to consider two surface first one is base circular surface and dome shape surface

Surface 1 is flat and thus $F_11$=0

From summation rule :$F_11$+$F_12$=1→$F_12$=1

From reciprocity rule: $A_1$ $F_12$=$A_2$ $F_21$

→$F_21$=$\frac{A_1}{A_2}$ $F_12$

=$\frac{A_1}{A_2}$ .1

=$\frac{(\frac{πD^2}{4})}{(\frac{πD^2}{2})}$=$\frac{1}{2}$=0.5

ii)For two concentric cylinders

We number different surfaces as

The outer surface of the inner cylinder (1)

The inner surface of the outer cylinder (2)

No radiation leaving surface 1 strikes itself and thus $F_11$=0

All radiation leaving surface 1 strikes surface 2 and thus $F_12$=1 From reciprocity rule:

$A_1$ $F_12$=$A_2$ $F_(21 $)

$F_21$=$\frac{A_1}{A_2}$ $F_12$

=$\frac{(πD_1 h)}{(πD_2 h)}$.1=$\frac{D_1}{D_2}$

Summation rule:

$F_21$+$F_22$=1

$F_22$=1-$F_21$

=1-$\frac{D_1}{D_2}$