Question

pls help!

using washer method: Find the volume of the solid generated by revolving the region bounded by y = sqrtx, y=0, and x=3, about the y-axis.

Answer 1

First: a quick review. The area of a washer of inside radius ri and outside radius ro is

A = Pi( ro^2 -ri^2).

Since x=3 is one of the boundaries of the region, r0 = the outside radius=3 (constant).

The inside radius is found by solving y=Sqrt(x) for x: x=y^2=xi.

Then the area of a washer at distance y above the x-axis is A = Pi ( (3)^2 - (y^2)^2 ). Let its thickness be dy.

Then integrate the following from y=0 to y=Sqrt(3): Pi* ( (3)^2 - (y^2)^2 ) dy.