For her fitness class, Ana bought a stability ball that has a volume of 4,500π cubic inches. Fredrick is taking the same fitness class and needs a stability ball that is congruent to Ana's because he is the same height. What must the diameter of Fredrick's stability ball be for it to be congruent to Ana's?

Because Frederick's ball is congruent to Anna's, its volume should also be equal to 4,500π in³.

The volume of the spherical figure is calculated to the equation,

V = 4πr³/3

where r is the radius.

To get the value of r,

r = sqrt (3V/4π)

Substituting the known value of V,

r = sqrt ((3) (4,300π) / 4π)

r = 58.09 inches

Diameter is twice the measure of the radius,

D = 2 x 58.09 iches

D = 116.19 inches

Thus, the diameter of Fredrick's stability ball is approximately 116.19 inches.