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

Where is the table?

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.