Penguin huddling to withstand the harsh weather of the Antarctic, emperor penguins huddles in groups (Figure) assume that a penguin is a circular cylinder with a top surface area a = 0.34 m2 and height h = 1.1 m. Let Pr be the rate at which an individual penguin radiates energy to the environment (through the top and the sides); thus NP, is the rate at which N identical, well-separated penguins radiate. If the penguins huddle closely to form a huddled cylinder with top surface area Na and height h, the cylinder radiates at the rate Ph. If N = 1000,(a) What is the value of the fraction Ph/NPr and(b) By what percentage does huddling reduce the total radiationloss?