If the ratio of the length of the three edges of a cuboid passing through a vertex is 1:2:3, the diagonal length of the cuboid is 3 times, and 14 under the root sign, then the cuboid's volume is?

The length of three edges is x, 2x, 3x
√(1+2^2)=√5
√(3^2+5^2)=√34
3√14=√34x
x=3√(14/34)=(3/17)*√119
The volume of this cuboid is 6x ^ 3 = 1134 * √ 119 / 289

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