【正确答案】(1)所求的面积为
A=∫₀^2πaydx=∫₀^2πa(1一cost).a(1一cost)dt=a²∫₀^2π(1一cost)²dt=
=8a²∫₀^πsin⁴t dt=
(2)所求体积为
V=π∫₀^2πdy²dx=π∫₀^2πa²(1一cost)².a(1一cost)dt
==16πa³∫₀^πsin⁶tdt=