Final answer:
To find the volume of the solid generated by revolving the region enclosed by a triangle about the y-axis, we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region enclosed by the triangle (4,3), (4,5), and (7,5) about the y-axis, we can use the method of cylindrical shells. First, we need to find the height of the cylinder, which is the difference between the x-coordinates of the two vertices of the base (7 and 4). The radius of the cylindrical shell is the y-coordinate of the vertex (5). The volume of the cylindrical shell is given by the formula V = 2πrh, where r is the radius and h is the height. We can sum up the volumes of all the cylindrical shells to find the total volume of the solid.