How do you find the volume of the solid generated by revolving the region enclosed by the parabola y^2=4x and the line y=x revolved about the x-axis?

1 Answer
May 12, 2016

The problem is equivalent to:

find the volume of the solid generated by revolving the region enclosed by the parabola y = x^2/4 and the line x = y both revolted about the y axis. So
f_1(r)=r^2/4
f_2(r)=r
V_1(R) = 2pi int_0^R f_1(r)rdr
V_2(R) = 2pi int_0^R f_2(r)rdr
V(R) = V_2(R)-V_1(R)
R is such that f_1(r) = f_2(r) giving R = 4
So V(4) = 32pi/3