Question

I don't understand how to do this

Answer 1

Answer:

64$\pi$ 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 = $\pi$$r^{2}$

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

So,

A=$\frac{\pi r^{2} }{4}$

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= $\frac{16\pi }{4}$=$\frac{4\pi }{1}$=4$\pi$

Now lets get it back to $r^{2}$ by square rooting the 4

A=$\sqrt{4\pi }$=2$\pi$

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$\pi$ which simplifies to 64$\pi$

And a final answer of

64$\pi$ in²

Hope this helps :)