Answer:
Volume of cube= a^3
=(2/√3)^3
=8/3√3 cubic units. (~1.5396 cubic units)
Step-by-step explanation:
Such a cube has diagonal lengths (DF, AG, EC & HB)=diameter of sphere=2 units.
Let the sides of the cube (FG, GC, CB, BF, etc.) be 'a'.
Hence facial diagonal of the cube (FC, BG, FH, etc.) will be √2a (Pythagoras' Theorem).
Applying Pythagoras' theorem for △DFC:
FC²+DC²=FD²
⇒(√2a)²+a²=2²
⇒3a²=4
⇒a=2/√3 units
