题目

Life for Cathy Taylor’s three children is very busy. Their school days are busy enough. After school, though, Cathy takes the two boys from football to basketball. Then she has to take her daughter to piano lessons. The tired children don’t get home until 7 pm. They have a quick supper, and it’s time for homework.The Taylors are like many American and British parents. They take their children from activity to activity, and try to fit as much as possible into their kids’ lives. Doctors say many children are under too much pressure. Teachers complain(抱怨) about teaching tired kids in 14．如图，在四棱锥P-ABCD中，E是PC的中点，底面ABCD为矩形，AB=4，AD=2，△PAD为正三角形，且平面PAD⊥平面ABCD，平面ABE与棱PD交于点F，平面PCD与平面PAB交于直线l．（1）求证：l∥EF；（2）求三棱锥P-AEF的体积．