Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis. Region R is rotated about the line y=-2. Find the volume of Region R after being rotated.

The volume of the region after being rotated is 603.186 unit³

Step-by-step explanation:

Here we have the shape formed by the region is that of a hollow cylinder with thickness 4 and length 6 with radius of opening at center = 2

Therefore, the volume is

πR²L - πr²L = πL (R² - r²)

Where:

R = Outer radius of the cylinder = 4 + 2 = 6

r = inner radius = 2

L = Length of the cylinder = 6

Therefore we have

Volume = π*6 * (6² - 2²) = 603.186 unit³.