MHB Find the volume using shell and disk method

[jaychay]

Can you please help me ?
I have tried to do it but I end up getting the wrong answer.

 

[skeeter]

$\displaystyle V = 18\pi - 2\pi \int_0^{\pi/2} x \cos{x} \, dx$

$\displaystyle V = 18\pi - \pi \int_0^1 [\arccos{y}]^2 \, dy$

 

[jaychay]

$\displaystyle V = 18\pi - 2\pi \int_0^{\pi/2} x \cos{x} \, dx$

$\displaystyle V = 18\pi - \pi \int_0^1 [\arccos{y}]^2 \, dy$

Can you tell me where did 18 pi come from ?

 

[skeeter]

Can you tell me where did 18 pi come from ?

volume of a hemisphere is $\dfrac{2\pi r^3}{3}$ and $r = 3$