integration, area and volume

a) Find the area enclosed between y=1/sqrt(1-x^2), the x axis and the lines x=0 and x=1/2.

integrating y I got [sin^-1(x)] between limits 1/2 and 0 which equals

=[sin^-1(1/2)]-[sin^-1(0)]

=pi/6 units^2

b) This area is rotated about the y-axis. Find the exact volume of the soild formed.

This is what I am thinking...........use V= pi integral x^2 dy with limits pi/6 and 0. I rearranged y from part a) to make x^2 the subject and got x^2=1-y^-2.

Anywho I integrated and got V=5pi/4 units^3

The answer is pi/6(7sqrt(3)-12)units^3

I am way off, can someone please show me where I'm going wrong.

Thank you