# 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?

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## Question:

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?

30 inches

Step-by-step explanation:

As, the stability ball of Ana is congruent to the stability ball of Fredrick. This implies that the volume of both the balls will be same.

So, Volume of Ana’s ball = Volume of Fredrick’s ball = 4500 .

Now, the volume of a sphere is given by , where ‘r’ is the radius.

Substituting the value of the volume in this formula, we will obtain the radius.

i.e.

i.e.

i.e. r = 15 inches

As, diameter is the double of the radius.

So, diameter = 2×radius = 2×15 = 30 inches.

Hence, the diameter of Fredrick’s ball the 30 inches.

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