Question

Find the volume of the solid formed by revolving the region bounded by the graphs of y=4x^2 and y=16 about the x-axis. (Washer Volume)

Answer 1

integral from y = 0 to y = 16 (origin to x = 2)
find volume of outer cylinder of radius 16
Vol - pi r^2 h = pi (16^2) (2)

find volume generated by inner curve between x axis and y = 4 x^2
Vinner = pi y^2 dx from 0 to 2
= pi 16 * integral x^4 dx
= 16 pi (32/5)

then subtract the inner from the outer
2 pi (16^2) - 16 pi (32/5)

= 32 pi *16 - 32 pi *16/5

= 32 pi (4/5) (16)

Answer 2

Oh, double that to include the left side.