Question

Only need #2 plz i know the answer is B i just don’t know why

Answer 1

Check the picture below.

so, if we grab that sector made by UGD, like you see in the picture, we revolve it to the left-side and behind, we'll end up really with a half of a sphere, whose radius is 8.

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies V=\cfrac{4\pi 8^3}{3}\implies V=\cfrac{2048\pi }{3} \\\\\\ \stackrel{using~\pi =3.14}{V=2143.57}\implies \stackrel{\textit{half of that for a semi-sphere}}{V\approx 1071.78\overline{6}}\implies \stackrel{\textit{rounded up}}{V=1071.79}$

Answer 2

The rotation about UG would generate a hemisphere of radius 8. The volume of a sphere with radius $r$ is $\dfrac43\pi r^3$, so the volume of the hemisphere would be $\dfrac12\cdot\dfrac43\pi 8^3\approx\dfrac{1024\cdot3.14}3\approx1071.79$.