Buddy the Elf is busy wrapping gifts. rThis year, he is giving cylindrical containers lled with his favorite maple syrup. He has a sequence of cylindrical containers to ll and wrap aligned in order of size, starting with the largest. The rst container, C1, has a height of h and a radius of _ :0 n 1) hn_1 and i". For n > 1, the nth container has a height h.\" and radius Tn where hn : ( n n 1 p r\" = ( ) rn_1 for some p > 0. n. (a) Find formulas for n and T'n in terms of h and r. (b) Suppose p = 1, h = 1ft, and r = 1ft. I Buddy is stacking the containers as he lls them. Let H N be the total height of the stack after he lls the Nth container. Buddy\"s Christmas tree is 10 ft tall. Will Buddy's tower be taller than his Christmas tree? if not, explain why. If so, how many containers would it take? Explain your reasoning. I Buddy has 5 ft3 of syrup to put into the containers. Will he be able to t all of the syrup in his containers? If not, explainy why. If so, how many containers would it take? Explain your reasoning. (c) Suppose Buddy has an innite number of containers, but we do not know p, h- or v". Find the interval of p values for which the amount of syrup he can t inside the containers is nite, but the amount of wrapping paper needed to wrap the containers is innite