A5. The ratio of the body diagonal to the face diagonal in a cube is
(A) $\sqrt{2}: \sqrt{3}$
(B) $2: 3$
(C) $\sqrt{3}: \sqrt{2}$
(D) $3: 2$
(E) $\sqrt{2}: 1$
A5. If $a$ is the length of the edge of the surface, the length of the face diagonal is $\sqrt{a^{2}+a^{2}}=\sqrt{2} a$, and the space diagonal is $\sqrt{a^{2}+a^{2}+a^{2}}=\sqrt{3} a$, so the ratio between the space diagonal and the face diagonal is $\sqrt{3}: \sqrt{2}$.