How do we say "within a kilometer radius spherically"? When we say radius, we think of a circle, so how do you specify that you're thinking of a sphere when you say "within a kilometer radius"?
One could say "spherically", or "within a one-kilometer sphere". In some contexts the three-dimensionality will be obvious, as when one is speaking ot the relative position of satellites, say, or stars
- There are ten satellites within a fifty kilometer radius
- There are fewer than twelve stars within ten light-years of the sun.
But there is no special word or phrase that I know of for use in this situation, perhaps because it doesn't come up very often in ordinary speech.
Pretty much just like that. "Radius" is used for spheres as well as circles.
... anything inside a sphere of one-kilometer radius around the object.
Alternately, just say
... anything within one kilometer of the object
assuming it's obvious you're talking about spatial rather than surface distances.
You can say:
One kilometer in any direction.
I usually say 'within a spherical radius of x from this point'.
In 3d computing and visual effects, this comes up more often than you would think.
"Radius" is redundant. The term "within" already conveys the concept. If you want to emphasize that it's three dimensional, you can say that: "Within one kilometer, in any of the three dimensions".
We say this:
Within a ten-foot-square area.
Within a ten-foot-cube area.
The equivalent for a sphere, and extending it to a kilometre, would be:
Within a one-kilometre-sphere area.
Note that you can also add a d to the end of all of these (squared, cubed, and sphered). While the version without a d is more an adjective and the version with a d is more a verb, I've heard both square and squared, as well as cube and cubed, and I couldn't say if one is more obviously (and objectively) natural than the other. I simply used the adjectival version for all three of my examples.