optimization - Graph a series of planes as a solid object in Mathematica -

i'm trying graph series of planes solid object in mathematica. first tried use rangeplot3d options fill options graph 3d volume, unable find working result.

the graphic i'm trying create show deviation between z axis , radius origin of 3d cuboid. current equation i'm using this:

plot3d[evaluate[{sqrt[(c[1])^2 + x^2 + y^2]} /.  c[1] -> range[6378100, 6379120]], {x, -1000000,  1000000}, {y, -1000000, 1000000}, axeslabel -> automatic] 

(output more manageable range looks follows)

where c1 origional z-value @ each plane , result of equation z+(r-z) point on x,y plane.

however method incredibly inefficient. because used model large objects original z-values of >6,000,000 , heights above 1000, mathematica unable graph thousands of planes , represent them in responsive method.

additionally, because range of c1 includes integer values, there discontinuity between these planes.

is there way rewrite using different mathematica functionality generate 3dplot both reasonable load on system , smooth object?

2nd, can improve perforamance? when computing above input >30min, mathematica utilizing 30% cpu , 4gb of ram light load on graphics card well. twice as chrome using right on system.

i attempted enable cudalink, wouldn't enable properly. offer performance boost type of processing?

for reference, system build is: 16gb ram intel i7 4770k running @ stock settings nvidia geforce 760gtx 256 samsung ssd

plotting million planes , hoping becomes 3d solid seems unlikely succeed.

perhaps adapt this

show[plot3d[{sqrt[6^2+x^2+y^2], sqrt[20^2+x^2+y^2]}, {x, -10, 10}, {y, -10, 10},    axeslabel -> automatic, plotrange -> {{-15, 15}, {-15, 15}, all}],    graphics3d[{    polygon[join[     table[{x, -10, sqrt[6^2 + x^2 + (-10)^2]}, {x, -10, 10, 1}],      table[{x, -10, sqrt[20^2 + x^2 + (-10)^2]}, {x, 10, -10, -1}]]],     polygon[join[     table[{-10, y, sqrt[6^2 + (-10)^2 + y^2]}, {y, -10, 10, 1}],      table[{-10, y, sqrt[20^2 + (-10)^2 + y^2]}, {y, 10, -10, -1}]]],     polygon[join[     table[{x, 10, sqrt[6^2 + x^2 + 10^2]}, {x, -10, 10, 1}],      table[{x, 10, sqrt[20^2 + x^2 + 10^2]}, {x, 10, -10, -1}]]],     polygon[join[     table[{10, y, sqrt[6^2 + 10^2 + y^2]}, {y, -10, 10, 1}],      table[{10, y, sqrt[20^2 + 10^2 + y^2]}, {y, 10, -10, -1}]]]}]] 

what plot top , bottom surface , construct 4 polygons, each connecting top , bottom surface along 1 side. 1 caution, if very closely see that, because polygons, edges of 4 faces made of short line segments rather parabolas , not joining 2 paraboloids, there can tiny gaps or tiny overlaps. may or may not make difference application.

that graphic displays in fraction of second on machine fraction of yours.

mathematica not automatically parallelize computations onto multiple cores. cuda programming considerably bigger challenge turning link on. if can define each face of solid , combine them show think have greater chance of success.