Penguin huddling.To withstand the harsh weather of the Antartic, emperor penguins huddle in groups ( Figure ). Assume that a penguins is a circular cylinder with a top surface area a = `0.26 m^(2)` ,and height h = 90 cm. Let `P_(r )` be the rate at which an individual penduin radiates energy to the environment (through the top and the sides ), thus `NP_(r )` is the rate at which N identical, well separated penguins radiate. if the penduins radiate. If the penguis huddle closely to form a huddled cylinder with top surface area Na and height h, the cylinder radiates at the rate `P_(h)`. If N = 1000, (a) what is the value of the fraction `P_(h) //NP_(r )` and (b) by what percentage does huddling reduces the total radiation loss ?

Answer

(a) 0.17; (b) 0.83 or 83%