SAT Question c984f1a5: Area and Volume answer and explanation with Desmos solution

Choice D is correct. The volume, $V$, of a sphere is given by $V=\frac{4}{3}\pi r^3$, where $r$ is the radius of the sphere. Since a hemisphere is half of a sphere, it follows that the volume, $V$, of a hemisphere is given by $V=\left(\frac{1}{2}\right)\left(\frac{4}{3}\right)\pi r^3$, or $V=\frac{2}{3}\pi r^3$. Substituting $27$ for $r$ in this formula yields $V=\frac{2}{3}\pi {\left(27\right)}^3$, which gives $V=13,122\pi$, or $V$ is approximately equal to $41,223.98$. Therefore, the choice that is closest to the volume, in cubic inches, of this hemisphere is $41,200$.