# The region between curves $y= {\sqrt x}$ , $0≤x≤4,y=1,x=4$ is revolved about $y=1$. Find the volume of a generated solid.

The region between curves $$y= {\sqrt x}$$ , $$0≤x≤4,y=1,x=4$$ is revolved about $$y=1$$. Find the volume of a generated solid.

I believe I need to find volume outlined by green, blue and dotted, black line (like on the graph).

$$V = \pi \int_1^4 ({\sqrt x})^2 \,dx$$. Is it correct approach or should I calculate $$\pi \int_0^4 ({\sqrt x})^2 \,dx$$ instead or maybe there is different approach.

Hint: You have to calculate $$\pi\int_1^4(\sqrt{x}-1)^2dx$$ which is the volume of the curve $$\sqrt{x}-1$$ revolved around $$y=0$$ instead.