Question

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1+ √x, the y-axis, and the line y = 3 about the line y = 5.

a) 13.333
b) 17.657
c) 41.888
d) None of these

Answer 1

Use the washer method

V= pi * integral of R^2 - r^2

R= 5- (1 +radx)
r= 5-3= 2

V= pi* integral of { (5- (1 +radx)) ^2 - 2^2 } from 0 to 4.

Answer 2

Or, using shells of thickness dy,
v = ∫[1,3] 2πrh dy
where r = 5-y and h = x = (y-1)^2
v = ∫[1,3] 2π(5-y)(y-1)^2 dy