How do you find the volume of solid formed by rotating the region bounded by the graphs: #y=sqrt(x)+5#; y=5; x=1; and x=0; around y=2?
Please see below.
The region described is shown below in blue. A representative slice is taken by the black line inside the region.The axis of rotation is the line
When the slice is rotated the result will be a thin disc (washer).
Let us denote the greater radius by
The volume of the disc (washer) will be
In this picture the thickness is
So the representative disc has volume
As the final step in setting up the integral, we note that
So the volume of the solid is