How to find the diameter of a sphere - ISEE Upper Level Quantitative Reasoning

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Question

There is a perfectly spherical weather balloon with a surface area of , what is its diameter?

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Answer

There is a perfectly spherical weather balloon with a surface area of , what is its diameter?

Begin with the formula for surface area of a sphere:

Now, set it equal to the given surface area and solve for r:

First divide both sides by .

Then square root both sides to get our radius:

Now, because the question is asking for our diameter and not our radius, we need to double our radius to get our answer:

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