Question

let r be a region in quadrant i with centroid (3, 5) and area 12 unit square. find the volume of the solid formed when this region is rotated around the y-axis.

Answer 1

To find the volume of the solid formed when this region is rotated around the y-axis, we can use the method of cylindrical shells. The volume of each shell is given by the formula V = 2πr*Δy, and the total volume is found by integrating the individual volumes over the range of y-values of the region.

Step-by-step explanation:

To find the volume of the solid formed when this region is rotated around the y-axis, we can use the method of cylindrical shells. We need to find the radius and height of each shell. The radius of each shell is the distance from the y-axis to a point on the region, which can be calculated using the x-coordinate of the centroid, and the height of each shell is the differential length along the y-axis. The volume of each shell is then given by the formula V = 2πr*Δy, and the total volume is found by integrating the individual volumes over the range of y-values of the region.