Asphere with a diameter of 9 units fits exactly in the clear glass cube as shown.
which expression represents the volume, in cubic units, of empty space in the cube?

a.π(4.53) – (4.5)3
b.(9)3 – π(4.52)
c.π(4.53) – (9)3
d.(9)3 – π(4.53)

The answer 
for solving such a problem, the volume, in cubic units, of empty space in the cube must be the result of the difference of the volume of the sphere and the cube.

the volume of sphere 
V= 4/3 x π x R^3
it is V= 4/3 x π x  4.5^3, because the diameter = 9, and from where R= diameter / 2 = 4.5

the value of V is V= 4/3π(4.5)^3

 the volume of the cube

V= length ^3= 9^3 =243

so,  the  volume of empty space = (9)3 - 4/3π(4.5)^3

the true answer is (9)3 - 4/3π(4.5)^3

The correct answer is addition