# ACT Aspire Math: Defining the Relationship Between Radius and Area

The radii of two circles have a ratio of 1:4.

What is the ratio of their areas?

ACT Aspire | Math |

ACT Aspire Math | Geometry |

Math | Geometry |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

would win a pie fight until we realized that this

problem doesn't even have any pie to settle the score

Well if two similar circles have radio in the ratio

of eight to be than their areas are in the

ratio of a swear to be squared and their volumes

Aaron the ratio a cube to be cubed But that's

a math factoid to save for a party that needs

livening up the areas of two circles in question have

a ratio of one squared to four squared which is

equivalent to a ratio of one to sixteen So if

you didn't remember this rule while you can also set

up a ratio using the area formula pi r squared

and you know your own numbers maintaining the ratio of

radio i wonder for a while we can imagine that

the first circle has a radius of two and the

second circle a radius of eight First circle would then

have an area of pi r squared or four pi

and the second circle would have an area of pie

eight squared or sixty four pi Well just cut out

the pie Serve yourself a slice and find the ratio

of four to sixty for which then simplifies to yes 00:01:23.812 --> [endTime] one to sixteen so the answer is d