volume of a cylindrical solid

Consider my diagram. Let $r$ be the radius of the small circle and $R$ be the radius of the big circle.

$y+r=\dfrac{2r+9}{2}$

$2y+2r=2r+9$

$2y=9$

$y=4.5$

$5+x=y+r$

$5+x=4.5+r$

$r=0.5+x$ $\color{#D61F06}(1)$

By pythagorean theorem, we have

$r^2=x^2+y^2$ $\color{#D61F06}(2)$

Substitute $y=4.5$ and $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$(0.5+x)^2=x^2+4.5^2$

$0.25+x+x^2=x^2+20.25$

$x=20$

It follows that, $r=0.5+20=20.5$

Then, $R=OB=x+5=25$ .

The area of the shaded portion is $A_{s}=\pi(R^2-r^2)=\dfrac{22}{7}(25^2-20.5^2)=643.5$ .

Therefore, the volume is $643.5(8)=\color{#3D99F6}\boxed{5148}$