A sphere is perfectly round, and a cone has a circular base and a single point. In both shapes, the radius $r$ is the key measurement, while a cone also uses vertical height $h$ and sometimes slant height $l$.

The diameter goes all the way across a circle or sphere, so $d=2r$ and $r=\frac{d}{2}$. Most sphere and cone formulas use $r$, so always halve the diameter first if that is what the diagram gives you.

Volume measures the space inside a shape, and surface area measures the outside. For cones, volume uses the vertical height but surface area uses the slant height.