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?

Answer:

Answer:

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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