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one, if its a perfect sphere the radius will be constant whereever you measure it
It depends on the information you have. You could put the sphere on a flat surface and lower a horizontal plane onto it so that it just touches the top of the sphere. The distance between the flat surface and the horizontal plane is the sphere's diameter; the radius is half that. Or you could measure its volume by measuring the amount of fluid (water) that it displaces in a measuring container or the overflow from any full container. Then use the formula V = 4/3*pi*R3 to work out the radius. If you knew the density of the material of the sphere, you could measure its mass and work out its volume that way.
We can't say how many degrees there are in a sphere, any more than we can say how many feet there are in an acre. Feet are a measure of length, and an acre is an area, not a length. You can't measure an area with a tape measure. Likewise, degrees are a measure of an angle; you can sweep out a circle by swinging a line through an angle of 360 degrees. But you can't sweep out a sphere by swinging a line through some angle, so angle measure won't do to measure a sphere.
calculate the volume using the formula: Vsphere = (4/3)*pi*r^3 then calculate density by Density = Mass/Volume
measure the radius of the sphere and apply the appropriate volume equation: V= (4/3) x (pi) x r3