Question 46·200 Super-Hard SAT Math Questions·Geometry and Trigonometry

Let $r$ be the radius, from the base’s center to its edge, and $h$ be the height between the bases. A cylinder’s volume is $\pi r^2h$, so the given volume gives $100\pi=\pi r^2h$.

Each circular base has area $\pi r^2$, and the curved side has area $2\pi rh$. Total surface area includes both bases, so $90\pi=2\pi r^2+2\pi rh$.

The diameter is twice the radius, or $2r$. So height less than diameter means $h<2r$. Use this condition to choose between cylinders that fit both equations.

Type both equations in Desmos, using $x$ for radius and $y$ for height. Click the two intersections, where both equations hold, with positive radius: about $(2.62,14.53)$ and $(5,4)$. The first fails because $14.53>2(2.62)$. The second passes because $4<2(5)$, so its height is $4$ units. Choice A.