Consider the radial field f = (x, y, z) and let s be the sphere of radius a centered at the origin. compute the outward flux of f across s using the representation z = +_√a^2 - x^2 - y^2 for the sphere (either symmetry or two surfaces must be used.)

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step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

it would rotate about 180 degrees.