Answer:
511.8 cubic inches
Step-by-step explanation:
The volume of a sphere is given by ...
V = (4/3)πr³ = (4/3)π(d/2)³ = (π/6)d³ . . . . where d is the diameter
Assuming the dimension of the cube-shaped box is d, the diameter of the ball, the volume of the box will be d³. So, we have ...
85.3π = (π/6)d³
(85.3π)(6/π) = d³ . . . . . the volume of the box
(85.3)(6) = d³ = 511.8 . . . . cubic inches
The volume of the smallest box is 511.8 cubic inches.
