I don't understand how to do this

Answer:

64[tex]\pi[/tex] in²

Step-by-step explanation:

I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.

Remember,

A = [tex]\pi[/tex][tex]r^{2}[/tex]

And if we have 4 circles that means the area of one circle is 1/4th the total

So,

A=[tex]\frac{\pi r^{2} }{4}[/tex]

Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.

A= [tex]\frac{16\pi }{4}[/tex]=[tex]\frac{4\pi }{1}[/tex]=4[tex]\pi[/tex]

Now lets get it back to [tex]r^{2}[/tex] by square rooting the 4

A=[tex]\sqrt{4\pi }[/tex]=2[tex]\pi[/tex]

The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.

This gives us a final radius of the bigger circle of 8

Therefore, the area of the bigger circle is 8²[tex]\pi[/tex] which simplifies to 64[tex]\pi[/tex]

And a final answer of

64[tex]\pi[/tex] in²

Hope this helps :)

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