Question

I don't understand how to do this

Answer 1

64
`\pi` in²

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=
`(\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=
`(16\pi )/(4)`=
`(4\pi )/(1)`=4
`\pi`

Now lets get it back to
`r^(2)` by square rooting the 4

A=
`√(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 :)