课程名称︰微积分甲上
课程性质︰大一必修
课程教师︰朱桦
开课学院：电资学院、工学院
开课系所︰电机系、材料系
考试日期（年月日）︰2014/12/29
考试时限（分钟）：20 mins
试题 :
CALCULUS QUIZ 6
Instructor: Professor Huah Chu
Quiz date: 29, December, 2014
Quiz time: 20 minutes (备注: 但实际考试时,助教有延5分钟收卷)
Total score: 24 points (Each problem is worth 3 points).
Department: Name: Student ID :
Let C be the curve dened by x^(2/3)+y^(2/3) = 1 and R be the region
enclosed by C.
(a) Find the area of R.
(b) Find the length of the curve C.
(c) Find the volume of the solid generated by rotating R about the x-axis.
(d) Find the volume of the solid generated by rotating R about the y-axis.
(e) Find the area of the surface generated by rotating C about the x-axis.
(f) Find the area of the surface generated by rotating C about the y-axis.