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This object  is known  as the frustum  of a right circular cone .

The volume is given by :

pi * height  ( r₂^2 + r₁r₂ + r₁^2 ) / 3

The height is not given but it is the leg of a right triangle  with the other leg  = 12 - 8  = 4

And  the hypotenuse = l  = 10

So  the height  is sqrt (10^2  - 4^2)  =  sqrt (100 - 16)  =  sqrt (84)  = 2sqrt (21)

So the volume is

pi * 2sqrt (21) * [ 12^2  + 8*12 + 8^2 ]  / 3  =

pi * 2sqrt (21) * [ 144 + 96 + 64] / 3  =

pi * 2sqrt (21) *  [ 304] / 3   =

[ (608/3) * sqrt (21) pi  ]    units ^3