根据短文内容，选择正确答案。

   Mike is seven years old now and begins(开始) to go to school. His father is a driver and takes him to school in his car. Mike studies very hard(努力地) and all his teachers like him very  much.
   One day, Miss White teaches the students to count from one to ten. Mike can count them. Miss White is happy and asks him, “How many people(人) are there(有) in your family, Mike?”
“Two, Miss White, ” Mike says.
“Who are they?”
“My father and mother.”
“Oh?” Miss White is surprised(吃惊地). She says, “But I think there are three people in your family—your father, your mother and you. Am I right?”
“No. I'm not at home now. I'm at school, you know!” Mike says.

在平面直角坐标系xOy中，曲线C的参数方程为 $\{\begin{array}{c}x=a+a\cos \beta \\ y=a\sin \beta \end{array}$ （a＞0，β为参数），以O为极点，x轴的正半轴为极轴，建立极坐标系，直线l的极坐标方程ρcos（θ﹣ $\frac{\pi }{3}$ ）= $\frac{3}{2}$ ．

（Ⅰ）若曲线C与l只有一个公共点，求a的值；

（Ⅱ）A，B为曲线C上的两点，且∠AOB= $\frac{\pi }{3}$ ，求△OAB的面积最大值．

材料一：南亚地区的北部地震频发，北京时间2015年4月25日，尼泊尔发生了里氏8．1级大地震（震中位置：

28°12′N，84°42′E），此次地震给首都加德满都（27°42′N，85°20′E）造成重大财产损失和严重人员伤亡。

材料二：“南亚局部地区政区图”、“板块分布示意图”