Volume of sphere = 4/3 pi r^3
Radius of Earth = diameter / 2 = 7918/2 = 3959 mi
Radius of Core = 760/2 = 380
Radius of Mantle = radius of earth - thickness of crust = 3959 - 5 = 3954
Volume of manltle = 4/3 pi rm^3 - 4/3 pi rc^3 rm = radius of mantle rc = radius of core
= 4/3 pi (rm^3 - rc^3)
= 4/3 pi (3954^3 - 380^3) = 2.587 x10^11 cu miles (approx)