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
`(4)/(3) \pi r^3`, so the area-to-volume ratio wold be


`(4\pi r^2)/( (4)/(3)\pi r^3 ) = (3(4\pi r^2))/(4(\pi r^3))`


`= (3\pi r^2)/(\pi r^3)\\\\ = (3)/(r)`

Where r is the radius of the sphere.