How to find the diameter of a sphere - ISEE Upper Level Mathematics Achievement

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Question

There is a perfectly spherical weather balloon with a surface area of $900 \pi ft^2$ , what is its diameter?

Answer

There is a perfectly spherical weather balloon with a surface area of $900 \pi ft^2$ , what is its diameter?

Begin with the formula for surface area of a sphere:

$SA_{sphere}=4 \pi r^2$

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

$900 \pi ft^2=4 \pi r^2$

First divide both sides by $4\pi$ .

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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