help!!! application of integral calculus?

Question

1.a variable square whose plane is perpendicular to the x-axis has 2 adjacent vertices on the parabola y^2=4ax. find the volume of the solid generated as the square moves from x=0 to x=a

2.find the area of the surface generated by revolving each of the fallowing areas about:

a.)x-axis
1. 3y=4x from x=0 to x=3
2. x=t^3-3t, y=3t^2 from t=0 to t=1

3.show that the surface area of a cone with base r and slant height s is pi*r*s

Answer 1

At a given x the side of the square is 2y =4 sqrt(ax) so the square has an area of4y^2=16 a x
the volume would be
Int(0,a) 16axdx = 8a^3
2)The volume is a cone with vertex at x=0 and base radius 4
(at x=3 y =4)
V=1/3pi*16*3=16*pi
2´) V= Int(0,1)pi*(y)^2dx and dx = (3t^2-3)dt
V= 9*pi int(0,1)(3t^6-3t^2)dt = 27pi(1/7-1/3) (take the abs val.
=36/7*pi(as for t from o to 1 x goes from 0 to -2)
3)The developed area is a sector with base 2pir and radius s the area is 2pirs/2 = pi*r*s