Hi there, I am trying to solve this question, I got the volume formula as $r^2 \sin \theta \ \mathrm{d} r \ \mathrm{d} \phi \ \mathrm{d} \theta$ but I can not come up with a surface area volume as the top surface facing the cone confuses me. Can anyone please help??
Also I have most of my code ready but I am having issues with the last part of it, should I ask it here as well or go to codestackexchange ??
Thank you
The spherical part of the surface area is
$$\int_{\pi/4}^{\pi/2}\int_{\pi/4}^{\pi/2}r^2\sin\theta d\theta d\phi=4\cdot\frac\pi4\int_{\pi/4}^{\pi/2}\sin\theta d\theta= \frac\pi{\sqrt2} $$
The volume of the spherical section is
$$\int_{\pi/4}^{\pi/2}\int_{\pi/4}^{\pi/2}\int_0^2r^2\sin\theta\> drd\theta d\phi= \frac{\sqrt2\pi}3 $$