Question

What is the surface area-to-volume ratio of the spherical barrel cactus

Answer 1

I can't speak to the cactus specifically, but any sphere has a surface area of $4\pi r^2$ and a volume of $\frac{4}{3} \pi r^3$, so the area-to-volume ratio wold be

$\frac{4\pi r^2}{ \frac{4}{3}\pi r^3 } = \frac{3(4\pi r^2)}{4(\pi r^3)}$

$= \frac{3\pi r^2}{\pi r^3}\\\\ = \frac{3}{r}$

Where r is the radius of the sphere.