Final answer:
To find the volume of the solid generated by revolving the region about the y-axis, we can use the formula for the volume of a solid of revolution. The volume of the solid generated by revolving the triangle about the y-axis is 2π.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region about the y-axis, we need to use the formula for the volume of a solid of revolution. The region enclosed by the triangle with vertices (0, 0), (1, 0), and (1, 2) is a right triangle with base 1 and height 2.
The volume of a solid generated by revolving the triangle about the y-axis can be found by integrating the cross-sectional area from y=0 to y=2.
The cross-sectional area of a solid of revolution is given by the formula A(y) = πr^2, where r is the distance from the y-axis to the curve at height y. In this case, the distance from the y-axis to the right side of the triangle is 1, so the cross-sectional area is A(y) = π(1^2) = π.
Integrating the cross-sectional area from y=0 to y=2, we get the volume of the solid as V = ∫[0,2] A(y) dy = ∫[0,2] π dy = π[2-0] = 2π.