# 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?

##### 1 Answer

Please see below.

#### Explanation:

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