>626
xy-平面に平行な平面z=cで切った断面は、
　ただし　x^2≦y≦√c,　ただし c^2≦x≦c^(1/4),
　断面積は S(c) = ∫[c^2,c^(1/4)] {(√c) - x^2}dx = [(√c)x - (1/3)x^3](x=c^2,c^(1/4)) = (2/3)c^(3/4) - c^(5/2) + (1/3)c^6,
　V = ∫[0,1] S(z)dz = ∫[0,1] {(2/3)z^(3/4) - z^(5/2) + (1/3)z^6}dz = [ (8/21)z^(7/4) - (2/7)z^(7/2) + (1/21)z^7 ](z=0,1) = 8/21 - 2/7 + 1/21 = 1/7.

注)　0 ≦ x^8 ≦ y^4 ≦ z^2 ≦ x より 0 ≦ x^7 ≦1, 0 ≦ x ≦1.