Question

The four small circles are identical. The total area of the small circles is 64pi square inches. What is the area of the larger circle? Write your answer in terms of pi .

Answer 1

64 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 by square rooting the 4

`A=\sqrt4\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 which simplifies to 64

And a final answer of

64
`\pi` in²

Hope this helps :)