(A) Calculate the Power Transferred Through a 10 Cm Diameter $1 \mathrm {~m}$

(a) Calculate the power transferred through a 10 cm diameter iron rod that is $1 \mathrm {~m}$ long and is held at $0 ^ { \circ } \mathrm { C }$ on one end and $20 ^ { \circ } \mathrm { C }$ on the other end.
(b) It is desired to reduce the power transferred through the rod to $4 \mathrm {~W}$ by reducing the diameter of the rod. What should the new diameter be?