Since the formula for the area of a circle *squares the radius*, the area of the larger circle is always 4 (or 2^{2}) times the smaller circle. Think about it: You are doubling a number (which means ×2) and then squaring this (ie squaring 2) -- which leads to a new area that is four times the smaller one.

You can see this relationship is true if you pick some actual values for the radius of a circle.

For instance, let's make the original radius = 3 .

**Smaller Circle** |
**Larger Circle** |

radius $$ =3 $$ |
radius = $$3 \cdot 2 =6 $$ |

A = $$ \pi (3)^2 $$ |
A = $$ \pi (6)^2 $$ |

A = $$ 9 \pi $$ |
A = $$ 36 \pi $$ |

$$ A_{larger} = \color{red}{4} \cdot A_{smaller}
\\
A_{larger} = \color{red}{4} \cdot 9\pi
\\
A_{larger} = 36 \pi
$$

This relationship holds true no matter what radius you pick.

Let's make the original radius = 5.

Smaller Circle |
Larger Circle |

radius $$ =5$$ |
radius $$ =5 \cdot 2= 10$$ |

A = $$ \pi (5)^2 $$ |
A = $$ \pi (10)^2 $$ |

A = $$ 25 \pi $$ |
A = $$ 100 \pi $$ |

$$ A_{larger} = \color{red}{4} \cdot A_{smaller}
\\
A_{larger} = \color{red}{4} \cdot 25\pi
\\
A_{larger} = 100 \pi
$$