Question

Given the volume of a cube is 8 cubic meters, find

the distance from any vertex to the center point
inside the cube.
(A) 1 m
(B) √2 m
(C) 2√2 m
(D) 2√3 m
(E) √3 m

Answer 1

`V=8m^3\\\\V=a^3\\\\a^3=8m^3\to a=\sqrt[3]{8m^3}=2m\\\\diagonal\ of\ a\ cube:D=a\sqrt3\\\\D=2\sqrt3m\\\\Distance\ from\ any\ vertex\ to\ the\ center\ point\ inside\ the\ cube\\is\ a\ half\ of\ a\ diagonal:\\2\sqrt3:2=\sqrt3\ (m)\\\\Answer:E`